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Mathematics and Statistics Theses and Dissertations

Theses/dissertations from 2024 2024.

The Effect of Fixed Time Delays on the Synchronization Phase Transition , Shaizat Bakhytzhan

On the Subelliptic and Subparabolic Infinity Laplacian in Grushin-Type Spaces , Zachary Forrest

Utilizing Machine Learning Techniques for Accurate Diagnosis of Breast Cancer and Comprehensive Statistical Analysis of Clinical Data , Myat Ei Ei Phyo

Quandle Rings, Idempotents and Cocycle Invariants of Knots , Dipali Swain

Comparative Analysis of Time Series Models on U.S. Stock and Exchange Rates: Bayesian Estimation of Time Series Error Term Model Versus Machine Learning Approaches , Young Keun Yang

Theses/Dissertations from 2023 2023

Classification of Finite Topological Quandles and Shelves via Posets , Hitakshi Lahrani

Applied Analysis for Learning Architectures , Himanshu Singh

Rational Functions of Degree Five That Permute the Projective Line Over a Finite Field , Christopher Sze

Theses/Dissertations from 2022 2022

New Developments in Statistical Optimal Designs for Physical and Computer Experiments , Damola M. Akinlana

Advances and Applications of Optimal Polynomial Approximants , Raymond Centner

Data-Driven Analytical Predictive Modeling for Pancreatic Cancer, Financial & Social Systems , Aditya Chakraborty

On Simultaneous Similarity of d-tuples of Commuting Square Matrices , Corey Connelly

Symbolic Computation of Lump Solutions to a Combined (2+1)-dimensional Nonlinear Evolution Equation , Jingwei He

Boundary behavior of analytic functions and Approximation Theory , Spyros Pasias

Stability Analysis of Delay-Driven Coupled Cantilevers Using the Lambert W-Function , Daniel Siebel-Cortopassi

A Functional Optimization Approach to Stochastic Process Sampling , Ryan Matthew Thurman

Theses/Dissertations from 2021 2021

Riemann-Hilbert Problems for Nonlocal Reverse-Time Nonlinear Second-order and Fourth-order AKNS Systems of Multiple Components and Exact Soliton Solutions , Alle Adjiri

Zeros of Harmonic Polynomials and Related Applications , Azizah Alrajhi

Combination of Time Series Analysis and Sentiment Analysis for Stock Market Forecasting , Hsiao-Chuan Chou

Uncertainty Quantification in Deep and Statistical Learning with applications in Bio-Medical Image Analysis , K. Ruwani M. Fernando

Data-Driven Analytical Modeling of Multiple Myeloma Cancer, U.S. Crop Production and Monitoring Process , Lohuwa Mamudu

Long-time Asymptotics for mKdV Type Reduced Equations of the AKNS Hierarchy in Weighted L 2 Sobolev Spaces , Fudong Wang

Online and Adjusted Human Activities Recognition with Statistical Learning , Yanjia Zhang

Theses/Dissertations from 2020 2020

Bayesian Reliability Analysis of The Power Law Process and Statistical Modeling of Computer and Network Vulnerabilities with Cybersecurity Application , Freeh N. Alenezi

Discrete Models and Algorithms for Analyzing DNA Rearrangements , Jasper Braun

Bayesian Reliability Analysis for Optical Media Using Accelerated Degradation Test Data , Kun Bu

On the p(x)-Laplace equation in Carnot groups , Robert D. Freeman

Clustering methods for gene expression data of Oxytricha trifallax , Kyle Houfek

Gradient Boosting for Survival Analysis with Applications in Oncology , Nam Phuong Nguyen

Global and Stochastic Dynamics of Diffusive Hindmarsh-Rose Equations in Neurodynamics , Chi Phan

Restricted Isometric Projections for Differentiable Manifolds and Applications , Vasile Pop

On Some Problems on Polynomial Interpolation in Several Variables , Brian Jon Tuesink

Numerical Study of Gap Distributions in Determinantal Point Process on Low Dimensional Spheres: L -Ensemble of O ( n ) Model Type for n = 2 and n = 3 , Xiankui Yang

Non-Associative Algebraic Structures in Knot Theory , Emanuele Zappala

Theses/Dissertations from 2019 2019

Field Quantization for Radiative Decay of Plasmons in Finite and Infinite Geometries , Maryam Bagherian

Probabilistic Modeling of Democracy, Corruption, Hemophilia A and Prediabetes Data , A. K. M. Raquibul Bashar

Generalized Derivations of Ternary Lie Algebras and n-BiHom-Lie Algebras , Amine Ben Abdeljelil

Fractional Random Weighted Bootstrapping for Classification on Imbalanced Data with Ensemble Decision Tree Methods , Sean Charles Carter

Hierarchical Self-Assembly and Substitution Rules , Daniel Alejandro Cruz

Statistical Learning of Biomedical Non-Stationary Signals and Quality of Life Modeling , Mahdi Goudarzi

Probabilistic and Statistical Prediction Models for Alzheimer’s Disease and Statistical Analysis of Global Warming , Maryam Ibrahim Habadi

Essays on Time Series and Machine Learning Techniques for Risk Management , Michael Kotarinos

The Systems of Post and Post Algebras: A Demonstration of an Obvious Fact , Daviel Leyva

Reconstruction of Radar Images by Using Spherical Mean and Regular Radon Transforms , Ozan Pirbudak

Analyses of Unorthodox Overlapping Gene Segments in Oxytricha Trifallax , Shannon Stich

An Optimal Medium-Strength Regularity Algorithm for 3-uniform Hypergraphs , John Theado

Power Graphs of Quasigroups , DayVon L. Walker

Theses/Dissertations from 2018 2018

Groups Generated by Automata Arising from Transformations of the Boundaries of Rooted Trees , Elsayed Ahmed

Non-equilibrium Phase Transitions in Interacting Diffusions , Wael Al-Sawai

A Hybrid Dynamic Modeling of Time-to-event Processes and Applications , Emmanuel A. Appiah

Lump Solutions and Riemann-Hilbert Approach to Soliton Equations , Sumayah A. Batwa

Developing a Model to Predict Prevalence of Compulsive Behavior in Individuals with OCD , Lindsay D. Fields

Generalizations of Quandles and their cohomologies , Matthew J. Green

Hamiltonian structures and Riemann-Hilbert problems of integrable systems , Xiang Gu

Optimal Latin Hypercube Designs for Computer Experiments Based on Multiple Objectives , Ruizhe Hou

Human Activity Recognition Based on Transfer Learning , Jinyong Pang

Signal Detection of Adverse Drug Reaction using the Adverse Event Reporting System: Literature Review and Novel Methods , Minh H. Pham

Statistical Analysis and Modeling of Cyber Security and Health Sciences , Nawa Raj Pokhrel

Machine Learning Methods for Network Intrusion Detection and Intrusion Prevention Systems , Zheni Svetoslavova Stefanova

Orthogonal Polynomials With Respect to the Measure Supported Over the Whole Complex Plane , Meng Yang

Theses/Dissertations from 2017 2017

Modeling in Finance and Insurance With Levy-It'o Driven Dynamic Processes under Semi Markov-type Switching Regimes and Time Domains , Patrick Armand Assonken Tonfack

Prevalence of Typical Images in High School Geometry Textbooks , Megan N. Cannon

On Extending Hansel's Theorem to Hypergraphs , Gregory Sutton Churchill

Contributions to Quandle Theory: A Study of f-Quandles, Extensions, and Cohomology , Indu Rasika U. Churchill

Linear Extremal Problems in the Hardy Space H p for 0 p , Robert Christopher Connelly

Statistical Analysis and Modeling of Ovarian and Breast Cancer , Muditha V. Devamitta Perera

Statistical Analysis and Modeling of Stomach Cancer Data , Chao Gao

Structural Analysis of Poloidal and Toroidal Plasmons and Fields of Multilayer Nanorings , Kumar Vijay Garapati

Dynamics of Multicultural Social Networks , Kristina B. Hilton

Cybersecurity: Stochastic Analysis and Modelling of Vulnerabilities to Determine the Network Security and Attackers Behavior , Pubudu Kalpani Kaluarachchi

Generalized D-Kaup-Newell integrable systems and their integrable couplings and Darboux transformations , Morgan Ashley McAnally

Patterns in Words Related to DNA Rearrangements , Lukas Nabergall

Time Series Online Empirical Bayesian Kernel Density Segmentation: Applications in Real Time Activity Recognition Using Smartphone Accelerometer , Shuang Na

Schreier Graphs of Thompson's Group T , Allen Pennington

Cybersecurity: Probabilistic Behavior of Vulnerability and Life Cycle , Sasith Maduranga Rajasooriya

Bayesian Artificial Neural Networks in Health and Cybersecurity , Hansapani Sarasepa Rodrigo

Real-time Classification of Biomedical Signals, Parkinson’s Analytical Model , Abolfazl Saghafi

Lump, complexiton and algebro-geometric solutions to soliton equations , Yuan Zhou

Theses/Dissertations from 2016 2016

A Statistical Analysis of Hurricanes in the Atlantic Basin and Sinkholes in Florida , Joy Marie D'andrea

Statistical Analysis of a Risk Factor in Finance and Environmental Models for Belize , Sherlene Enriquez-Savery

Putnam's Inequality and Analytic Content in the Bergman Space , Matthew Fleeman

On the Number of Colors in Quandle Knot Colorings , Jeremy William Kerr

Statistical Modeling of Carbon Dioxide and Cluster Analysis of Time Dependent Information: Lag Target Time Series Clustering, Multi-Factor Time Series Clustering, and Multi-Level Time Series Clustering , Doo Young Kim

Some Results Concerning Permutation Polynomials over Finite Fields , Stephen Lappano

Hamiltonian Formulations and Symmetry Constraints of Soliton Hierarchies of (1+1)-Dimensional Nonlinear Evolution Equations , Solomon Manukure

Modeling and Survival Analysis of Breast Cancer: A Statistical, Artificial Neural Network, and Decision Tree Approach , Venkateswara Rao Mudunuru

Generalized Phase Retrieval: Isometries in Vector Spaces , Josiah Park

Leonard Systems and their Friends , Jonathan Spiewak

Resonant Solutions to (3+1)-dimensional Bilinear Differential Equations , Yue Sun

Statistical Analysis and Modeling Health Data: A Longitudinal Study , Bhikhari Prasad Tharu

Global Attractors and Random Attractors of Reaction-Diffusion Systems , Junyi Tu

Time Dependent Kernel Density Estimation: A New Parameter Estimation Algorithm, Applications in Time Series Classification and Clustering , Xing Wang

On Spectral Properties of Single Layer Potentials , Seyed Zoalroshd

Theses/Dissertations from 2015 2015

Analysis of Rheumatoid Arthritis Data using Logistic Regression and Penalized Approach , Wei Chen

Active Tile Self-assembly and Simulations of Computational Systems , Daria Karpenko

Nearest Neighbor Foreign Exchange Rate Forecasting with Mahalanobis Distance , Vindya Kumari Pathirana

Statistical Learning with Artificial Neural Network Applied to Health and Environmental Data , Taysseer Sharaf

Radial Versus Othogonal and Minimal Projections onto Hyperplanes in l_4^3 , Richard Alan Warner

Ensemble Learning Method on Machine Maintenance Data , Xiaochuang Zhao

Theses/Dissertations from 2014 2014

Properties of Graphs Used to Model DNA Recombination , Ryan Arredondo

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Megamenu featured, megamenu social, math/stats thesis and colloquium topics.

Updated: April 2024

Math/Stats Thesis and Colloquium Topics 2024- 2025

The degree with honors in Mathematics or Statistics is awarded to the student who has demonstrated outstanding intellectual achievement in a program of study which extends beyond the requirements of the major. The principal considerations for recommending a student for the degree with honors will be: Mastery of core material and skills, breadth and, particularly, depth of knowledge beyond the core material, ability to pursue independent study of mathematics or statistics, originality in methods of investigation, and, where appropriate, creativity in research.

An honors program normally consists of two semesters (MATH/STAT 493 and 494) and a winter study (WSP 031) of independent research, culminating in a thesis and a presentation. Under certain circumstances, the honors work can consist of coordinated study involving a one semester (MATH/STAT 493 or 494) and a winter study (WSP 030) of independent research, culminating in a “minithesis” and a presentation. At least one semester should be in addition to the major requirements, and thesis courses do not count as 400-level senior seminars.

An honors program in actuarial studies requires significant achievement on four appropriate examinations of the Society of Actuaries.

Highest honors will be reserved for the rare student who has displayed exceptional ability, achievement or originality. Such a student usually will have written a thesis, or pursued actuarial honors and written a mini-thesis. An outstanding student who writes a mini-thesis, or pursues actuarial honors and writes a paper, might also be considered. In all cases, the award of honors and highest honors is the decision of the Department.

Here is a list of possible colloquium topics that different faculty are willing and eager to advise. You can talk to several faculty about any colloquium topic, the sooner the better, at least a month or two before your talk. For various reasons faculty may or may not be willing or able to advise your colloquium, which is another reason to start early.

RESEARCH INTERESTS OF MATHEMATICS AND STATISTICS FACULTY

Here is a list of faculty interests and possible thesis topics.  You may use this list to select a thesis topic or you can use the list below to get a general idea of the mathematical interests of our faculty.

Colin Adams (On Leave 2024 – 2025)

Research interests:   Topology and tiling theory.  I work in low-dimensional topology.  Specifically, I work in the two fields of knot theory and hyperbolic 3-manifold theory and develop the connections between the two. Knot theory is the study of knotted circles in 3-space, and it has applications to chemistry, biology and physics.  I am also interested in tiling theory and have been working with students in this area as well.

Hyperbolic 3-manifold theory utilizes hyperbolic geometry to understand 3-manifolds, which can be thought of as possible models of the spatial universe.

Possible thesis topics:

• Investigate various aspects of virtual knots, a generalization of knots.
• Consider hyperbolicity of virtual knots, building on previous SMALL work. For which virtual knots can you prove hyperbolicity?
• Investigate why certain virtual knots have the same hyperbolic volume.
• Consider the minimal Turaev volume of virtual knots, building on previous SMALL work.
• Investigate which knots have totally geodesic Seifert surfaces. In particular, figure out how to interpret this question for virtual knots.
• Investigate n-crossing number of knots. An n-crossing is a crossing with n strands of the knot passing through it. Every knot can be drawn in a picture with only n-crossings in it. The least number of n-crossings is called the n-crossing number. Determine the n-crossing number for various n and various families of knots.
• An übercrossing projection of a knot is a projection with just one n-crossing. The übercrossing number of a knot is the least n for which there is such an übercrossing projection. Determine the übercrossing number for various knots, and see how it relates to other traditional knot invariants.
• A petal projection of a knot is a projection with just one n-crossing such that none of the loops coming out of the crossing are nested. In other words, the projection looks like a daisy. The petal number of a knot is the least n for such a projection. Determine petal number for various knots, and see how it relates to other traditional knot invariants.
• In a recent paper, we extended petal number to virtual knots. Show that the virtual petal number of a classical knot is equal to the classical petal number of the knot (This is a GOOD question!)
• Similarly, show that the virtual n-crossing number of a classical knot is equal to the classical n-crossing number. (This is known for n = 2.)
• Find tilings of the branched sphere by regular polygons. This would extend work of previous research students. There are lots of interesting open problems about something as simple as tilings of the sphere.
• Other related topics.

Possible colloquium topics : Particularly interested in topology, knot theory, graph theory, tiling theory and geometry but will consider other topics.

Christina Athanasouli

Research Interests:   Differential equations, dynamical systems (both smooth and non-smooth), mathematical modeling with applications in biological and mechanical systems

My research focuses on analyzing mathematical models that describe various phenomena in Mathematical Neuroscience and Engineering. In particular, I work on understanding 1) the underlying mechanisms of human sleep (e.g. how sleep patterns change with development or due to perturbations), and 2) potential design or physical factors that may influence the dynamics in vibro-impact mechanical systems for the purpose of harvesting energy. Mathematically, I use various techniques from dynamical systems and incorporate both numerical and analytical tools in my work. 

Possible colloquium topics:   Topics in applied mathematics, such as:

• Mathematical modeling of sleep-wake regulation
• Mathematical modeling vibro-impact systems
• Bifurcations/dynamics of mathematical models in Mathematical Neuroscience and Engineering
• Bifurcations in piecewise-smooth dynamical systems

Julie Blackwood

Research Interests:   Mathematical modeling, theoretical ecology, population biology, differential equations, dynamical systems.

My research uses mathematical models to uncover the complex mechanisms generating ecological dynamics, and when applicable emphasis is placed on evaluating intervention programs. My research is in various ecological areas including ( I ) invasive species management by using mathematical and economic models to evaluate the costs and benefits of control strategies, and ( II ) disease ecology by evaluating competing mathematical models of the transmission dynamics for both human and wildlife diseases.

• Mathematical modeling of invasive species
• Mathematical modeling of vector-borne or directly transmitted diseases
• Developing mathematical models to manage vector-borne diseases through vector control
• Other relevant topics of interest in mathematical biology

Each topic (1-3) can focus on a case study of a particular invasive species or disease, and/or can investigate the effects of ecological properties (spatial structure, resource availability, contact structure, etc.) of the system.

Possible colloquium topics:   Any topics in applied mathematics, such as:

Research Interest :  Statistical methodology and applications.  One of my research topics is variable selection for high-dimensional data.  I am interested in traditional and modern approaches for selecting variables from a large candidate set in different settings and studying the corresponding theoretical properties. The settings include linear model, partial linear model, survival analysis, dynamic networks, etc.  Another part of my research studies the mediation model, which examines the underlying mechanism of how variables relate to each other.  My research also involves applying existing methods and developing new procedures to model the correlated observations and capture the time-varying effect.  I am also interested in applications of data mining and statistical learning methods, e.g., their applications in analyzing the rhetorical styles in English text data.

• Variable selection uses modern techniques such as penalization and screening methods for several different parametric and semi-parametric models.
• Extension of the classic mediation models to settings with correlated, longitudinal, or high-dimensional mediators. We could also explore ways to reduce the dimensionality and simplify the structure of mediators to have a stable model that is also easier to interpret.
• We shall analyze the English text dataset processed by the Docuscope environment with tools for corpus-based rhetorical analysis. The data have a hierarchical structure and contain rich information about the rhetorical styles used. We could apply statistical models and statistical learning algorithms to reduce dimensions and gain a more insightful understanding of the text.

Possible colloquium topics:  I am open to any problems in statistical methodology and applications, not limited to my research interests and the possible thesis topics above.

Richard De Veaux 

Research interests: Statistics.

My research interests are in both statistical methodology and in statistical applications.  For the first, I look at different methods and try to understand why some methods work well in particular settings, or more creatively, to try to come up with new methods.  For the second, I work in collaboration with an investigator (e.g. scientist, doctor, marketing analyst) on a particular statistical application.  I have been especially interested in problems dealing with large data sets and the associated modeling tools that work for these problems.

• Human Performance and Aging.I have been working on models for assessing the effect of age on performance in running and swimming events. There is still much work to do. So far I’ve looked at masters’ freestyle swimming and running data and a handicapped race in California, but there are world records for each age group and other events in running and swimming that I’ve not incorporated. There are also many other types of events.
• Variable Selection.  How do we choose variables when we have dozens, hundreds or even thousands of potential predictors? Various model selection strategies exist, but there is still a lot of work to be done to find out which ones work under what assumptions and conditions.
• Problems at the interface.In this era of Big Data, not all methods of classical statistics can be applied in practice. What methods scale up well, and what advances in computer science give insights into the statistical methods that are best suited to large data sets?
• Applying statistical methods to problems in science or social science.In collaboration with a scientist or social scientist, find a problem for which statistical analysis plays a key role.

Possible colloquium topics:

• Almost any topic in statistics that extends things you’ve learned in courses —  specifically topics in Experimental design, regression techniques or machine learning
• Model selection problems

Thomas Garrity (On Leave 2024 – 2025)

Research interest:   Number Theory and Dynamics.

My area of research is officially called “multi-dimensional continued fraction algorithms,” an area that touches many different branches of mathematics (which is one reason it is both interesting and rich).  In recent years, students writing theses with me have used serious tools from geometry, dynamics, ergodic theory, functional analysis, linear algebra, differentiability conditions, and combinatorics.  (No single person has used all of these tools.)  It is an area to see how mathematics is truly interrelated, forming one coherent whole.

While my original interest in this area stemmed from trying to find interesting methods for expressing real numbers as sequences of integers (the Hermite problem), over the years this has led to me interacting with many different mathematicians, and to me learning a whole lot of math.  My theses students have had much the same experiences, including the emotional rush of discovery and the occasional despair of frustration.  The whole experience of writing a thesis should be intense, and ultimately rewarding.   Also, since this area of math has so many facets and has so many entrance points, I have had thesis students from wildly different mathematical backgrounds do wonderful work; hence all welcome.

• Generalizations of continued fractions.
• Using algebraic geometry to study real submanifolds of complex spaces.

Possible colloquium topics:   Any interesting topic in mathematics.

Leo Goldmakher

Research interests:   Number theory and arithmetic combinatorics.

I’m interested in quantifying structure and randomness within naturally occurring sets or sequences, such as the prime numbers, or the sequence of coefficients of a continued fraction, or a subset of a vector space. Doing so typically involves using ideas from analysis, probability, algebra, and combinatorics.

Possible thesis topics:  

Anything in number theory or arithmetic combinatorics.

Possible colloquium topics:   I’m happy to advise a colloquium in any area of math.

Susan Loepp

Research interests: Commutative Algebra.  I study algebraic structures called commutative rings.  Specifically, I have been investigating the relationship between local rings and their completion.  One defines the completion of a ring by first defining a metric on the ring and then completing the ring with respect to that metric.  I am interested in what kinds of algebraic properties a ring and its completion share.  This relationship has proven to be intricate and quite surprising.  I am also interested in the theory of tight closure, and Homological Algebra.

Topics in Commutative Algebra including:

• Using completions to construct Noetherian rings with unusual prime ideal structures.
• What prime ideals of C[[ x 1 ,…, x n ]] can be maximal in the generic formal fiber of a ring? More generally, characterize what sets of prime ideals of a complete local ring can occur in the generic formal fiber.
• Characterize what sets of prime ideals of a complete local ring can occur in formal fibers of ideals with height n where n ≥1.
• Characterize which complete local rings are the completion of an excellent unique factorization domain.
• Explore the relationship between the formal fibers of R and S where S is a flat extension of R .
• Determine which complete local rings are the completion of a catenary integral domain.
• Determine which complete local rings are the completion of a catenary unique factorization domain.

Possible colloquium topics:   Any topics in mathematics and especially commutative algebra/ring theory.

Steven Miller

For more information and references, see http://www.williams.edu/Mathematics/sjmiller/public_html/index.htm

Research interests :  Analytic number theory, random matrix theory, probability and statistics, graph theory.

My main research interest is in the distribution of zeros of L-functions.  The most studied of these is the Riemann zeta function, Sum_{n=1 to oo} 1/n^s.  The importance of this function becomes apparent when we notice that it can also be written as Prod_{p prime} 1 / (1 – 1/p^s); this function relates properties of the primes to those of the integers (and we know where the integers are!).  It turns out that the properties of zeros of L-functions are extremely useful in attacking questions in number theory.  Interestingly, a terrific model for these zeros is given by random matrix theory: choose a large matrix at random and study its eigenvalues.  This model also does a terrific job describing behavior ranging from heavy nuclei like Uranium to bus routes in Mexico!  I’m studying several problems in random matrix theory, which also have applications to graph theory (building efficient networks).  I am also working on several problems in probability and statistics, especially (but not limited to) sabermetrics (applying mathematical statistics to baseball) and Benford’s law of digit bias (which is often connected to fascinating questions about equidistribution).  Many data sets have a preponderance of first digits equal to 1 (look at the first million Fibonacci numbers, and you’ll see a leading digit of 1 about 30% of the time).  In addition to being of theoretical interest, applications range from the IRS (which uses it to detect tax fraud) to computer science (building more efficient computers).  I’m exploring the subject with several colleagues in fields ranging from accounting to engineering to the social sciences.

Possible thesis topics: 

• Theoretical models for zeros of elliptic curve L-functions (in the number field and function field cases).
• Studying lower order term behavior in zeros of L-functions.
• Studying the distribution of eigenvalues of sets of random matrices.
• Exploring Benford’s law of digit bias (both its theory and applications, such as image, voter and tax fraud).
• Propagation of viruses in networks (a graph theory / dynamical systems problem). Sabermetrics.
• Additive number theory (questions on sum and difference sets).

Possible colloquium topics: 

Plus anything you find interesting.  I’m also interested in applications, and have worked on subjects ranging from accounting to computer science to geology to marketing….

Ralph Morrison

Research interests:   I work in algebraic geometry, tropical geometry, graph theory (especially chip-firing games on graphs), and discrete geometry, as well as computer implementations that study these topics. Algebraic geometry is the study of solution sets to polynomial equations.  Such a solution set is called a variety.  Tropical geometry is a “skeletonized” version of algebraic geometry. We can take a classical variety and “tropicalize” it, giving us a tropical variety, which is a piecewise-linear subset of Euclidean space.  Tropical geometry combines combinatorics, discrete geometry, and graph theory with classical algebraic geometry, and allows for developing theory and computations that tell us about the classical varieties.  One flavor of this area of math is to study chip-firing games on graphs, which are motivated by (and applied to) questions about algebraic curves.

Possible thesis topics : Anything related to tropical geometry, algebraic geometry, chip-firing games (or other graph theory topics), and discrete geometry.  Here are a few specific topics/questions:

• Study the geometry of tropical plane curves, perhaps motivated by results from algebraic geometry.  For instance:  given 5 (algebraic) conics, there are 3264 conics that are tangent to all 5 of them.  What if we look at tropical conics–is there still a fixed number of tropical conics tangent to all of them?  If so, what is that number?  How does this tropical count relate to the algebraic count?
• What can tropical plane curves “look like”?  There are a few ways to make this question precise.  One common way is to look at the “skeleton” of a tropical curve, a graph that lives inside of the curve and contains most of the interesting data.  Which graphs can appear, and what can the lengths of its edges be?  I’ve done lots of work with students on these sorts of questions, but there are many open questions!
• What can tropical surfaces in three-dimensional space look like?  What is the version of a skeleton here?  (For instance, a tropical surface of degree 4 contains a distinguished polyhedron with at most 63 facets. Which polyhedra are possible?)
• Study the geometry of tropical curves obtained by intersecting two tropical surfaces.  For instance, if we intersect a tropical plane with a tropical surface of degree 4, we obtain a tropical curve whose skeleton has three loops.  How can those loops be arranged?  Or we could intersect degree 2 and degree 3 tropical surfaces, to get a tropical curve with 4 loops; which skeletons are possible there?
• One way to study tropical geometry is to replace the usual rules of arithmetic (plus and times) with new rules (min and plus).  How do topics like linear algebra work in these fields?  (It turns out they’re related to optimization, scheduling, and job assignment problems.)
• Chip-firing games on graphs model questions from algebraic geometry.  One of the most important comes in the “gonality” of a graph, which is the smallest number of chips on a graph that could eliminate (via a series of “chip-firing moves”) an added debt of -1 anywhere on the graph.  There are lots of open questions for studying the gonality of graphs; this include general questions, like “What are good lower bounds on gonality?” and specific ones, like “What’s the gonality of the n-dimensional hypercube graph?”
• We can also study versions of gonality where we place -r chips instead of just -1; this gives us the r^th gonality of a graph.  Together, the first, second, third, etc. gonalities form the “gonality sequence” of a graph.  What sequences of integers can be the gonality sequence of some graph?  Is there a graph whose gonality sequence starts 3, 5, 8?
• There are many computational and algorithmic questions to ask about chip-firing games.  It’s known that computing the gonality of a general graph is NP-hard; what if we restrict to planar graphs?  Or graphs that are 3-regular? And can we implement relatively efficient ways of computing these numbers, at least for small graphs?
• What if we changed our rules for chip-firing games, for instance by working with chips modulo N?  How can we “win” a chip-firing game in that context, since there’s no more notion of debt?
• Study a “graph throttling” version of gonality.  For instance, instead of minimizing the number of chips we place on the graph, maybe we can also try to decrease the number of chip-firing moves we need to eliminate debt.
• Chip-firing games lead to interesting questions on other topics in graph theory.  For instance, there’s a conjectured upper bound of (|E|-|V|+4)/2 on the gonality of a graph; and any graph is known to have gonality at least its tree-width.  Can we prove the (weaker) result that (|E|-|V|+4)/2 is an upper bound on tree-width?  (Such a result would be of interest to graph theorists, even the idea behind it comes from algebraic geometry!)
• Topics coming from discrete geometry.  For example:  suppose you want to make “string art”, where you have one shape inside of another with string weaving between the inside and the outside shapes.  For which pairs of shapes is this possible?

Possible Colloquium topics:   I’m happy to advise a talk in any area of math, but would be especially excited about talks related to algebra, geometry, graph theory, or discrete mathematics.

Shaoyang Ning (On Leave 2024 – 2025)

Research Interest :  Statistical methodologies and applications. My research focuses on the study and design of statistical methods for integrative data analysis, in particular, to address the challenges of increasing complexity and connectivity arising from “Big Data”. I’m interested in innovating statistical methods that efficiently integrate multi-source, multi-resolution information to solve real-life problems. Instances include tracking localized influenza with Google search data and predicting cancer-targeting drugs with high-throughput genetic profiling data. Other interests include Bayesian methods, copula modeling, and nonparametric methods.

• Digital (disease) tracking: Using Internet search data to track and predict influenza activities at different resolutions (nation, region, state, city); Integrating other sources of digital data (e.g. Twitter, Facebook) and/or extending to track other epidemics and social/economic events, such as dengue, presidential approval rates, employment rates, and etc.
• Predicting cancer drugs with multi-source profiling data: Developing new methods to aggregate genetic profiling data of different sources (e.g., mutations, expression levels, CRISPR knockouts, drug experiments) in cancer cell lines to identify potential cancer-targeting drugs, their modes of actions and genetic targets.
• Social media text mining: Developing new methods to analyze and extract information from social media data (e.g. Reddit, Twitter). What are the challenges in analyzing the large-volume but short-length social media data? Can classic methods still apply? How should we innovate to address these difficulties?
• Copula modeling: How do we model and estimate associations between different variables when they are beyond multivariate Normal? What if the data are heavily dependent in the tails of their distributions (commonly observed in stock prices)? What if dependence between data are non-symmetric and complex? When the size of data is limited but the dimension is large, can we still recover their correlation structures? Copula model enables to “link” the marginals of a multivariate random variable to its joint distribution with great flexibility and can just be the key to the questions above.
• Other cross-disciplinary, data-driven projects: Applying/developing statistical methodology to answer an interesting scientific question in collaboration with a scientist or social scientist.

Possible colloquium topics:   Any topics in statistical methodology and application, including but not limited to: topics in applied statistics, Bayesian methods, computational biology, statistical learning, “Big Data” mining, and other cross-disciplinary projects.

Anna Neufeld

Research interests:  My research is motivated by the gap between classical statistical tools and practical data analysis. Classic statistical tools are designed for testing a single hypothesis about a single, pre-specified model. However, modern data analysis is an adaptive process that involves exploring the data, fitting several models, evaluating these models, and then testing a potentially large number of hypotheses about one or more selected models. With this in mind, I am interested in topics such as (1) methods for model validation and selection, (2) methods for testing data-driven hypotheses (post-selection inference), and (3) methods for testing a large number of hypotheses. I am also interested in any applied project where I can help a scientist rigorously answer an important question using data. 

• Cross-validation for unsupervised learning. Cross-validation is one of the most widely-used tools for model validation, but, in its typical form, it cannot be used for unsupervised learning problems. Numerous ad-hoc proposals exist for validating unsupervised learning models, but there is a need to compare and contrast these proposals and work towards a unified approach.
• Identifying the number of cell types in single-cell genomics datasets. This is an application of the topic above, since the cell types are typically estimated via unsupervised learning.
• There is growing interest in “post-prediction inference”, which is the task of doing valid statistical inference when some inputs to your statistical model are the outputs of other statistical models (i.e. predictions). Frameworks have recently been proposed for post-prediction inference in the setting where you have access to a gold-standard dataset where the true inputs, rather than the predicted inputs, have been observed. A thesis could explore the possibility of post-prediction inference in the absence of this gold-standard dataset.
• Any other topic of student interest related to selective inference, multiple testing, or post-prediction inference.
• Any collaborative project in which we work with a scientist to identify an interesting question in need of non-standard statistics.
• I am open to advising colloquia in almost any area of statistical methodology or applications, including but not limited to: multiple testing, post-selection inference, post-prediction inference, model selection, model validation, statistical machine learning, unsupervised learning, or genomics.

Allison Pacelli

Research interests:   Math Education, Math & Politics, and Algebraic Number Theory.

Math Education.  Math education is the study of the practice of teaching and learning mathematics, at all levels. For example, do high school calculus students learn best from lecture or inquiry-based learning? What mathematical content knowledge is critical for elementary school math teachers? Is a flipped classroom more effective than a traditional learning format? Many fascinating questions remain, at all levels of education. We can talk further to narrow down project ideas.

Math & Politics.  The mathematics of voting and the mathematics of fair division are two fascinating topics in the field of mathematics and politics. Research questions look at types of voting systems, and the properties that we would want a voting system to satisfy, as well as the idea of fairness when splitting up a single object, like cake, or a collection of objects, such as after a divorce or a death.

Algebraic Number Theory.  The Fundamental Theorem of Arithmetic states that the ring of integers is a unique factorization domain, that is, every integer can be uniquely factored into a product of primes. In other rings, there are analogues of prime numbers, but factorization into primes is not necessarily unique!

In order to determine whether factorization into primes is unique in the ring of integers of a number field or function field, it is useful to study the associated class group – the group of equivalence classes of ideals. The class group is trivial if and only if the ring is a unique factorization domain. Although the study of class groups dates back to Gauss and played a key role in the history of Fermat’s Last Theorem, many basic questions remain open.

  Possible thesis topics:

• Topics in math education, including projects at the elementary school level all the way through college level.
• Topics in voting and fair division.
• Investigating the divisibility of class numbers or the structure of the class group of quadratic fields and higher degree extensions.
• Exploring polynomial analogues of theorems from number theory concerning sums of powers, primes, divisibility, and arithmetic functions.

Possible colloquium topics:   Anything in number theory, algebra, or math & politics.

Anna Plantinga

Research interests:   I am interested in both applied and methodological statistics. My research primarily involves problems related to statistical analysis within genetics, genomics, and in particular the human microbiome (the set of bacteria that live in and on a person).  Current areas of interest include longitudinal data, distance-based analysis methods such as kernel machine regression, high-dimensional data, and structured data.

• Impacts of microbiome volatility. Sometimes the variability of a microbial community is more indicative of an unhealthy community than the actual bacteria present. We have developed an approach to quantifying microbiome variability (“volatility”). This project will use extensive simulations to explore the impact of between-group differences in volatility on a variety of standard tests for association between the microbiome and a health outcome.
• Accounting for excess zeros (sparse feature matrices). Often in a data matrix with many zeros, some of the zeros are “true” or “structural” zeros, whereas others are simply there because we have fewer observations for some subjects. How we account for these zeros affects analysis results. Which methods to account for excess zeros perform best for different analyses?
• Longitudinal methods for compositional data. When we have longitudinal data, we assume the same variables are measured at every time point. For high-dimensional compositions, this may not be the case. We would generally assume that the missing component was absent at any time points for which it was not measured. This project will explore alternatives to making that assumption.
• Applied statistics research. In collaboration with a scientist or social scientist, use appropriate statistical methodology (or variations on existing methods) to answer an interesting scientific question.

Any topics in statistical application, education, or methodology, including but not restricted to:

• Topics in applied statistics.
• Methods for microbiome data analysis.
• Statistical genetics.
• Electronic health records.
• Variable selection and statistical learning.
• Longitudinal methods.

Cesar Silva

Research interests :  Ergodic theory and measurable dynamics; in particular mixing properties and rank one examples, and infinite measure-preserving and nonsingular transformations and group actions.  Measurable dynamics of transformations defined on the p-adic field.  Measurable sensitivity.  Fractals.  Fractal Geometry.

Possible thesis topics:    Ergodic Theory.   Ergodic theory studies the probabilistic behavior of abstract dynamical systems.  Dynamical systems are systems that change with time, such as the motion of the planets or of a pendulum.  Abstract dynamical systems represent the state of a dynamical system by a point in a mathematical space (phase space).  In many cases this space is assumed to be the unit interval [0,1) with Lebesgue measure.  One usually assumes that time is measured at discrete intervals and so the law of motion of the system is represented by a single map (or transformation) of the phase space [0,1).  In this case one studies various dynamical behaviors of these maps, such as ergodicity, weak mixing, and mixing.  I am also interested in studying the measurable dynamics of systems defined on the p-adics numbers.  The prerequisite is a first course in real analysis.  Topological Dynamics.  Dynamics on compact or locally compact spaces.

Topics in mathematics and in particular:

• Any topic in measure theory.  See for example any of the first few chapters in “Measure and Category” by J. Oxtoby. Possible topics include the Banach-Tarski paradox, the Banach-Mazur game, Liouville numbers and s-Hausdorff measure zero.
• Topics in applied linear algebra and functional analysis.
• Fractal sets, fractal generation, image compression, and fractal dimension.
• Dynamics on the p-adic numbers.
• Banach-Tarski paradox, space filling curves.

Mihai Stoiciu

Research interests: Mathematical Physics and Functional Analysis. I am interested in the study of the spectral properties of various operators arising from mathematical physics – especially the Schrodinger operator. In particular, I am investigating the distribution of the eigenvalues for special classes of self-adjoint and unitary random matrices.

Topics in mathematical physics, functional analysis and probability including:

• Investigate the spectrum of the Schrodinger operator. Possible research topics: Find good estimates for the number of bound states; Analyze the asymptotic growth of the number of bound states of the discrete Schrodinger operator at large coupling constants.
• Study particular classes of orthogonal polynomials on the unit circle.
• Investigate numerically the statistical distribution of the eigenvalues for various classes of random CMV matrices.
• Study the general theory of point processes and its applications to problems in mathematical physics.

Possible colloquium topics:  

Any topics in mathematics, mathematical physics, functional analysis, or probability, such as:

• The Schrodinger operator.
• Orthogonal polynomials on the unit circle.
• Statistical distribution of the eigenvalues of random matrices.
• The general theory of point processes and its applications to problems in mathematical physics.

Elizabeth Upton

Research Interests: My research interests center around network science, with a focus on regression methods for network-indexed data. Networks are used to capture the relationships between elements within a system. Examples include social networks, transportation networks, and biological networks. I also enjoy tackling problems with pragmatic applications and am therefore interested in applied interdisciplinary research.

• Regression models for network data: how can we incorporate network structure (and dependence) in our regression framework when modeling a vertex-indexed response?
• Identify effects shaping network structure. For example, in social networks, the phrase “birds of a feather flock together” is often used to describe homophily. That is, those who have similar interests are more likely to become friends. How can we capture or test this effect, and others, in a regression framework when modeling edge-indexed responses?
• Extending models for multilayer networks. Current methodologies combine edges from multiple networks in some sort of weighted averaging scheme. Could a penalized multivariate approach yield a more informative model?
• Developing algorithms to make inference on large networks more efficient.
• Any topic in linear or generalized linear modeling (including mixed-effects regression models, zero-inflated regressions, etc.).
• Applied statistics research. In collaboration with a scientist or social scientist, use appropriate statistical methodology to answer an interesting scientific question.
• Any applied statistics research project/paper
• Topics in linear or generalized linear modeling
• Network visualizations and statistics

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Home > Mathematics and Statistics > MathStat TDs > Masters Theses

Mathematics and Statistics Masters Theses

Theses from 2024 2024.

A new proper orthogonal decomposition method with second difference quotients for the wave equation , Andrew Calvin Janes

The deep bsde method , Daniel Kovach

Theses from 2023 2023

THE APPLICATION OF STATISTICAL MODELING TO IDENTIFY GENETIC ASSOCIATIONS WITH MILD TRAUMATIC BRAIN INJURY OUTCOMES , Caroline Schott

META-ANALYSIS OF MESENCHYMAL STEM CELL GENE EXPRESSION MICROARRAY DATA FROM OBESE AND NON-OBESE PATIENTS , Dakota William Shields

Theses from 2022 2022

Continuous and discrete models for optimal harvesting in fisheries , Nagham Abbas Al Qubbanchee

Several problems in nonlinear Schrödinger equations , Tim Van Hoose

Theses from 2020 2020

Decoupled finite element methods for general steady two-dimensional Boussinesq equations , Lioba Boveleth

Quantifying effects of sleep deprivation on cognitive performance , Quang Nghia Le

The application of machine learning models in the concussion diagnosis process , Sujit Subhash

Theses from 2019 2019

Less is more: Beating the market with recurrent reinforcement learning , Louis Kurt Bernhard Steinmeister

Theses from 2018 2018

Models for high dimensional spatially correlated risks and application to thunderstorm loss data in Texas , Tobias Merk

An investigation of the influence of the 2007-2009 recession on the day of the week effect for the S&P 500 and its sectors , Marcel Alwin Trick

Theses from 2017 2017

The pantograph equation in quantum calculus , Thomas Griebel

Comparing region level testing methods for differential DNA methylation analysis , Arnold Albert Harder

A review of random matrix theory with an application to biological data , Jesse Aaron Marks

Family-based association studies of autism in boys via facial-feature clusters , Luke Andrew Settles

Theses from 2016 2016

Pricing of geometric Asian options in general affine stochastic volatility models , Johannes Ruppert

On the double chain ladder for reserve estimation with bootstrap applications , Larissa Schoepf

Theses from 2015 2015

Some combinatorial applications of Sage, an open source program , Jessica Ruth Chowning

Day of the week effect in returns and volatility of the S&P 500 sector indices , Juan Liu

Application of loglinear models to claims triangle runoff data , Netanya Lee Martin

Theses from 2014 2014

Adaptive wavelet discretization of tensor products in H-Tucker format , Mazen Ali

An iterative algorithm for variational data assimilation problems , Xin Shen

Statistical analysis of sleep patterns in Drosophila melanogaster , Luyang Wang

Theses from 2013 2013

Statistical analysis of microarray data in sleep deprivation , Stephanie Marie Berhorst

Immersed finite element method for interface problems with algebraic multigrid solver , Wenqiang Feng

Theses from 2012 2012

Abel dynamic equations of the first and second kind , Sabrina Heike Streipert

Lattice residuability , Philip Theodore Thiem

Theses from 2011 2011

A time series approach to electric load modelling , Matthias Benjamin Noller

Theses from 2010 2010

Closed-form solutions to discrete-time portfolio optimization problems , Mathias Christian Goeggel

Inverse limits with upper semi-continuous set valued bonding functions: an example , Christopher David Jacobsen

Theses from 2009 2009

The analogue of the iterated logarithm for quantum difference equations , Karl Friedrich Ulrich

Theses from 2008 2008

Modeling particulate matter emissions indices at the Hartsfield-Jackson Atlanta International Airport , Lu Gan

The dynamic multiplier-accelerator model in economics , Julius Severi Heim

Dynamic equations with piecewise continuous argument , Christian Keller

Theses from 2007 2007

Ostrowski and Grüss inequalities on time scales , Thomas Matthews

The Black-Scholes equation in quantum calculus , Christian Müttel

Computerized proofs of hypergeometric identities: Methods, advances, and limitations , Paul Nathaniel Runnion

Screening for noise variables , Lisa Trautwein

Theses from 2006 2006

Distance function applications of object comparison in artificial vision systems , Christina Michelle Ayres

Sensitivity analysis on the relationship between alcohol abuse or dependence and wages , Tim Jensen

Sensitivity analysis on the relationship between alcohol abuse or dependence and annual hours worked , Stefan Koerner

Endogeneity bias and two-stage least squares: a simulation study , Xujun Wang

Theses from 2005 2005

Local compactness of the hyperspace of connected subsets , Robbie A. Beane

A sequential approach to supersaturated design , Angela Marie Jugan

Tests for gene-treatment interaction in microarray data analysis , Wanrong Yin

Theses from 2003 2003

Pricing of European options , Dirk Rohmeder

Prediction intervals for the binomial distribution with dependent trials , Florian Sebastian Rueck

Theses from 2002 2002

The use of a Marakov dependent Bernoulli process to model the relationship between employment status and drug use , Kathrin Koetting

Theses from 2000 2000

Inverse limits on [0,1] using sequences of piecewise linear unimodal bonding maps , Brian Edward Raines

Theses from 1998 1998

A two-stage step-stress accelerated life testing scheme , Phyllis E. Pound Singer

Theses from 1997 1997

Some properties of hereditarily indecomposable chainable continua , Thomas John Kacvinsky

Theses from 1996 1996

The Axiom of Choice, well-ordering property, Continuum Hypothesis, and other meta-mathematical considerations , Daniel Collins

Theses from 1994 1994

Approximate distributional results for tolerance limits and confidence limits on reliability based on the maximum likelihood estimators for the logistic distribution , Teriann Collins

Theses from 1986 1986

Investigating the output angular acceleration extrema of the planar four bar mechanism , Matthew H. Koebbe

Theses from 1984 1984

Approximating distributions in order restricted inference : the simple tree ordering , Tuan Anh Tran

Theses from 1982 1982

Goodness-of-fit for the Weibull distribution with unknown parameters and censored sampling. , Michael Edward Aho

Theses from 1979 1979

On L convergence of Fourier series. , William O. Bray

Theses from 1977 1977

Characterizations of inner product spaces. , John Lee Roy Williams

Theses from 1975 1975

A study of several substitution ciphers using mathematical models. , Wanda Louise Garner

Theses from 1974 1974

Models for molecular vibration , Allan Bruce Capps

The completions of local rings and their modules. , Christopher Scott Taber

Linear geometry , Phyllis L. Thomas

Theses from 1971 1971

Integrability of the sums of the trigonometric series 1/2 aₒ + ∞ [over] Σ [over] n=1 a n cos nΘ and ∞ [over] Σ [over] n=1 a n sin nΘ , John William Garrett

Inclusion theorems for boundary value problems for delay differential equations , Leon M. Hall

Theses from 1965 1965

A study of certain conservative sets for parameters in the linear statistical model , Roger Alan Chapin

Comparison of methods to select a probability model , Howard Lyndal Colburn

Latent class analysis and information retrieval , George Loyd Jensen

Linear and quadratic programming with more than one objective function , William John Lodholz

Tschebyscheff fitting with polynomials and nonlinear functions , George F. Luffel

Theses from 1964 1964

The effect of matrix condition in the solution of a system of linear algebraic equations. , Herbert R. Alcorn

Estimation and tabulation of bias coefficients for regression analysis in incompletely specified linear models. , Harry Kerry Edwards

A study of a method for selecting the best of two or more mathematical models , August J. Garver

A study of methods for estimating parameters in the model y(t) = A₁e -p₁t + A₂e -p₂t + ϵ , Gerald Nicholas Haas

A parameter perturbation procedure for obtaining a solution to systems of nonlinear equations. , James Carlton Helm

A study of stability of numerical solution for parabolic partial differential equations. , Tsang-Chi Huang

A numerical study of Van Der Pol's nonlinear differential equation for various values of the parameter E. , Charles C. Limbaugh

A study on estimating parameters restricted by linear inequalities , William Lawrence May

Minimization of Boolean functions. , Don Laroy Rogier

A method to give the best linear combination of order statistics to estimate the mean of any symmetric population , Robert M. Smith

On a numerical solution of Dirichlet type problems with singularity on the boundary. , Randall Loran Yoakum

Theses from 1963 1963

A study of methods for estimating parameters in rational polynomial models , Thomas B. Baird

Investigation of measures of ill-conditioning , Thomas D. Calton

A numerical approach to a Sturm-Liouville type problem with variable coefficients and its application to heat transfer and temperature prediction in the lower atmosphere. , Troyce Don Jones

A study of methods for determining confidence intervals for the mean of a normal distribution with unknown varience by comparison of average lengths , Karl Richard Kneile

Stability properties of various predictor corrector methods for solving ordinary differential equations numerically. , Charles Edward. Leslie

Mathematical techniques in the solution of boundary value problems. , Vincent Paul Pusateri

A modified algorithm for Henrici's solution of y' ' = f (x,y) , Frank Garnett Walters

Theses from 1962 1962

An investigation of Lehmer's method for finding the roots of polynomial equations using the Royal-McBee LGP-30 , James W. Joiner

Theses from 1931 1931

The spinning top , Aaron Jefferson Miles

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Applied Statistics

Current/past master's theses.

• Gabriel Marie Falconer-Stout Differentiating large mining projects in SSA to produce varying impacts on measured health outcomes in progress, Master's thesis in Biostatistics 
• Zhixuan Li Extending the eggCounts Package for Censored Data Analysis of Anthelmintic Resistance in progress, Master's thesis in Biostatistics 
• Delia Luana Schüpbach Analysis of spatio-temporal fly distribution patterns and influential factors 2024, Master's thesis in Mathematics 
• Georgy Astakhov Sample size calculation: Implementation of different scenarios for the online tool SampleSizeR 2024, Master's thesis in Biostatistics  PDF
• Jonas Raphael Füglistaler Estimating the non-reporting rate of animals used in preclinical research using meta-analytical approaches 2023, Master's thesis in Biostatistics  PDF
• Isidro Gonzalez Scale space multiresolution decomposition: an implementation for raster data with the Google Earth engine 2023, Master's thesis in Mathematics  PDF
• Lukas Nägeli Differential growth analysis of agricultural Aureobasidium pullulas isolates 2023, Master's thesis in Biostatistics  PDF
• Anouk Petitpierre Fusion of heterogeneous data sources in preclinical research – evaluation of ordinary and weighted least squares regression and a Bayesian hierarchical modeling approach in R and STAN 2023, Master's thesis in Biostatistics 
• Céline Fabienne Hofmann An EM Algorithm approach to GLM modeling with varying dispersion under censoring and truncation with an application in insurance claims 2023, Master's thesis in Mathematics  PDF
• Chiara Aruanno Analysis of estimation and optimization approaches for Spatial Processes 2022, Master's thesis in Mathematics 
• Ruben Scherrer Algorithms for the Simulation of Isotropic Gaussian Random Fields on the Sphere 2022, Master's thesis in Mathematics  PDF
• Annina Cincera The Consequences of Misspecification in Exponential Random Graph Models 2022, Master's thesis in Mathematics  PDF
• Thomas Fischer Direct Misspecification Using a Fully Parametrized Generalized Wendland Covariance Function 2022, Master's thesis in Biostatistics 
• Tengyingzi Ma Visual Streak Localization in Spectral Domain Optical Coherence Tomography Images of Minipics 2022, Master's thesis in Mathematics 
• Nicolas Huber Avoiding overfitting in additive Bayesian networks 2021, Master's thesis in Mathematics  PDF
• Stefan Willi Extensions of Backfitting to Mixed and Spatial Models 2021, Master's thesis in Mathematics 
• Oliver John Identification of Potential Risk Factors for Back Pain in Horses: An Analysis Using Additive Bayesian Networks 2021, Master's thesis in Biostatistics  PDF
• David Markwalder A comparison of information theoretic feature selection- and extraction methods 2020, Master's thesis in Mathematics 
• Audrey Yeo Clustering analysis of longitudinal data set 2020, Master's thesis in Biostatistics 
• Uriah Daugaard Analysis of Behaviors Affecting Predation Success in a Ciliate Predator-Prey System 2020, Master's thesis in Biostatistics 
• Sandar Felicity Lim Dynamic network analysis on social behavior of wild house mice 2019, Master's thesis in Biostatistics  PDF
• Josef Stocker Estimation of Gaussian Random Fields Using Generalized Wendland Functions 2019, Master's thesis in Mathematics 
• Natacha Bodenhausen Predicting fungal community composition based on soil properties 2019, Master's thesis in Biostatistics  PDF
• Jonas Fürstenberger Models for Short-Term Forecast of River Flooding 2019, Master's thesis in Mathematics 
• Tea Isler Small sample considerations for anthelmintic resistance tests 2018, Master's thesis in Biostatistics  PDF
• Cynthia Dukic An R Package Comparative Analysis Between bnlearn and abn 2018, Master's thesis in Mathematics 
• Christos Polysopoulos Cardiac Surgery and Blood Transfusion Products. What Does Really Matter? 2017, Master's thesis in Biostatistics  PDF
• Pierre Häberli Statistical Data Analysis and Forecasting of a Multinational Company's Production 2017, Master's thesis in Mathematics 
• Roman Flury Multiresolution Decomposition of Incomplete Random Signals - A Statistical Application of Sparse Matrix Calculus 2017, Master's thesis in Biostatistics  PDF
• Marco Reto Schleiniger Stan implementation of a parametric bootstrapping procedure for additive Bayesian network analysis 2017, Master's thesis in Biostatistics 
• Anja Fallegger Extension of the zero-inflated hierarchical models in the eggCounts package 2017, Master's thesis in Mathematics  PDF
• Servan Grüninger Does the Blue Bird Get the Flu? - Using Twitter for Flu Surveillance 2017, Master's thesis in Biostatistics  PDF
• Samuel Noll Two- and three-class ROC analysis. A comparison of statistical tests. 2017, Master's thesis in Mathematics  PDF
• Ursina Brunnhofer Identification of key data in stationary hospital bed-utilisation and application of queueing theory on optimal bed-occupancy 2017, Master's thesis in Mathematics 
• Andrea Meier Risk factor study of pododermatitis in rabbits using additive Bayesian networks 2017, Master's thesis in Biostatistics  PDF
• Thimo Schuster mrbsizerR - Scale space multiresolution analysis in R 2017, Master's thesis in Biostatistics  PDF
• Fabienne Schürch Spatial Interpolation for Huge Datasets: Concepts, Implementations and Illustrations 2016, Master's thesis in Mathematics 
• Fabian Frei Estimation by Transformation 2016, Master's thesis in Mathematics 
• Carina Schneider A spate of statistical tests to climate data validation 2016, Master's thesis in Mathematics  PDF
• Carlos Ochoa Pereira Novel semiparametric estimation method for the analysis of zero-inflated data: an application to the young forest records of the Swiss NFI 3 2015, Master's thesis in Biostatistics 
• Linna Du Vulnerability Analysis of European Windstorms 2015, Master's thesis in Mathematics  PDF
• Markus Hirschbühl Problem Analysis - MMANOVA Framework and Unbalanced Designs 2015, Master's thesis in Mathematics 
• Kaspar Mösinger An R implementation for huge spatiotemporal covariance matrices 2015, Master's thesis in Mathematics 
• Gabrielle Elaine Moser Spatial Aspects of Forest Monitoring Data and Surface Estimation: An Analysis of the Swiss NFI 2014, Master's thesis in Biostatistics 
• Sabine Güsewell Phenological responses to changing temperatures: representativeness and precision of results from the Swiss Phenological Network 2014, Master's thesis in Biostatistics 
• Maria Sereina Graber Phylogenetic comparative methods for discrete responses in evolutionary biology 2013, Master's thesis in Biostatistics  PDF
• Florian Gerber MSc thesis (Biostatistics, University of Zurich, 2013): Disease mapping with the Besag-York-Mollié model applied to a cancer and a worm infections dataset 2013, Master's thesis in Biostatistics 
• Stefan Purtschert Construction of bathymetric charts using spatial statistics 2012, Master's thesis in Mathematics 
• Rebekka Schibli Spatio-temporal homogeneity of a satellite-derived global radiation climatology 2011, Master's thesis in Biostatistics  PDF

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What do senior theses in Statistics look like?

This is a brief overview of thesis writing; for more information, please see our website here . Senior theses in Statistics cover a wide range of topics, across the spectrum from applied to theoretical. Typically, senior theses are expected to have one of the following three flavors:                                                                                                            

1. Novel statistical theory or methodology, supported by extensive mathematical and/or simulation results, along with a clear account of how the research extends or relates to previous related work.

2. An analysis of a complex data set that advances understanding in a related field, such as public health, economics, government, or genetics. Such a thesis may rely entirely on existing methods, but should give useful results and insights into an interesting applied problem.                                                                                 

3. An analysis of a complex data set in which new methods or modifications of published methods are required. While the thesis does not necessarily contain an extensive mathematical study of the new methods, it should contain strong plausibility arguments or simulations supporting the use of the new methods.

A good thesis is clear, readable, and well-motivated, justifying the applicability of the methods used rather than, for example, mechanically running regressions without discussing the assumptions (and whether they are plausible), performing diagnostics, and checking whether the conclusions make sense. 

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• Master's Thesis

As an integral component of the Master of Science in Statistical Science program, you can submit and defend a Master's Thesis. Your Master's Committee administers this oral examination. If you choose to defend a thesis, it is advisable to commence your research early, ideally during your second semester or the summer following your first year in the program. It's essential to allocate sufficient time for the thesis writing process. Your thesis advisor, who also serves as the committee chair, must approve both your thesis title and proposal. The final thesis work necessitates approval from all committee members and must adhere to the  Master's thesis requirements  set forth by the Duke University Graduate School.

Master’s BEST Award 

Each second-year Duke Master’s of Statistical Science (MSS) student defending their MSS thesis may be eligible for the  Master’s BEST Award . The Statistical Science faculty BEST Award Committee selects the awardee based on the submitted thesis of MSS thesis students, and the award is presented at the departmental graduation ceremony. 

Thesis Proposal

All second-year students choosing to do a thesis must submit a proposal (not more than two pages) approved by their thesis advisor to the Master's Director via Qualtrics by November 10th.  The thesis proposal should include a title,  the thesis advisor, committee members, and a description of your work. The description must introduce the research topic, outline its main objectives, and emphasize the significance of the research and its implications while identifying gaps in existing statistical literature. In addition, it can include some of the preliminary results. 

Committee members

MSS Students will have a thesis committee, which includes three faculty members - two must be departmental primary faculty, and the third could be from an external department in an applied area of the student’s interest, which must be a  Term Graduate Faculty through the Graduate School or have a secondary appointment with the Department of Statistical Science. All Committee members must be familiar with the Student’s work.  The department coordinates Committee approval. The thesis defense committee must be approved at least 30 days before the defense date.

Thesis Timeline and  Departmental Process:

Before defense:.

Intent to Graduate: Students must file an Intent to Graduate in ACES, specifying "Thesis Defense" during the application. For graduation deadlines, please refer to https://gradschool.duke.edu/academics/preparing-graduate .

Scheduling Thesis Defense: The student collaborates with the committee to set the date and time for the defense and communicates this information to the department, along with the thesis title. The defense must be scheduled during regular class sessions. Be sure to review the thesis defense and submission deadlines at https://gradschool.duke.edu/academics/theses-and-dissertations/

Room Reservations: The department arranges room reservations and sends confirmation details to the student, who informs committee members of the location.

Defense Announcement: The department prepares a defense announcement, providing a copy to the student and chair. After approval, it is signed by the Master's Director and submitted to the Graduate School. Copies are also posted on department bulletin boards.

Initial Thesis Submission: Two weeks before the defense, the student submits the initial thesis to the committee and the Graduate School. Detailed thesis formatting guidelines can be found at https://gradschool.duke.edu/academics/theses-and-dissertations.

Advisor Notification: The student requests that the advisor email [email protected] , confirming the candidate's readiness for defense. This step should be completed before the exam card appointment.

Format Check Appointment: One week before the defense, the Graduate School contacts the student to schedule a format check appointment. Upon approval, the Graduate School provides the Student Master’s Exam Card, which enables the student to send a revised thesis copy to committee members.

MSS Annual Report Form: The department provides the student with the MSS Annual Report Form to be presented at the defense.

Post Defense:

Communication of Defense Outcome: The committee chair conveys the defense results to the student, including any necessary follow-up actions in case of an unsuccessful defense.

In Case of Failure: If a student does not pass the thesis defense, the committee's decision to fail the student must be accompanied by explicit and clear comments from the chair, specifying deficiencies and areas that require attention for improvement.

Documentation: The student should ensure that the committee signs the Title Page, Abstract Page, and Exam Card.

Annual Report Form: The committee chair completes the Annual Report Form.

Master's Director Approval: The Master's director must provide their approval by signing the Exam Card.

Form Submission: Lastly, the committee chair is responsible for returning all completed and signed forms to the Department.

Final Thesis Submission: The student must meet the Graduate School requirement by submitting the final version of their Thesis to the Graduate School via ProQuest before the specified deadline. For detailed information, visit https://gradschool.duke.edu/academics/preparinggraduate .

• The Stochastic Proximal Distance Algorithm
• Logistic-tree Normal Mixture for Clustering Microbiome Compositions
• Inference for Dynamic Treatment Regimes using Overlapping Sampling Splitting
• Bayesian Modeling for Identifying Selection in B Cell Maturation
• Differentially Private Verification with Survey Weights
• Stable Variable Selection for Sparse Linear Regression in a Non-uniqueness Regime  
• A Cost-Sensitive, Semi-Supervised, and Active Learning Approach for Priority Outlier Investigation
• Bayesian Decoupling: A Decision Theory-Based Approach to Bayesian Variable Selection
• A Differentially Private Bayesian Approach to Replication Analysis
• Numerical Approximation of Gaussian-Smoothed Optimal Transport
• Computational Challenges to Bayesian Density Discontinuity Regression
• Hierarchical Signal Propagation for Household Level Sales in Bayesian Dynamic Models
• Logistic Tree Gaussian Processes (LoTgGaP) for Microbiome Dynamics and Treatment Effects
• Bayesian Inference on Ratios Subject to Differentially Private Noise
• Multiple Imputation Inferences for Count Data
• An Euler Characteristic Curve Based Representation of 3D Shapes in Statistical Analysis
• An Investigation Into the Bias & Variance of Almost Matching Exactly Methods
• Comparison of Bayesian Inference Methods for Probit Network Models
• Differentially Private Counts with Additive Constraints
• Multi-Scale Graph Principal Component Analysis for Connectomics
• MCMC Sampling Geospatial Partitions for Linear Models
• Bayesian Dynamic Network Modeling with Censored Flow Data  
• An Application of Graph Diffusion for Gesture Classification
• Easy and Efficient Bayesian Infinite Factor Analysis
• Analyzing Amazon CD Reviews with Bayesian Monitoring and Machine Learning Methods
• Missing Data Imputation for Voter Turnout Using Auxiliary Margins
• Generalized and Scalable Optimal Sparse Decision Trees
• Construction of Objective Bayesian Prior from Bertrand’s Paradox and the Principle of Indifference
• Rethinking Non-Linear Instrumental Variables
• Clustering-Enhanced Stochastic Gradient MCMC for Hidden Markov Models
• Optimal Sparse Decision Trees
• Bayesian Density Regression with a Jump Discontinuity at a Given Threshold
• Forecasting the Term Structure of Interest Rates: A Bayesian Dynamic Graphical Modeling Approach
• Testing Between Different Types of Poisson Mixtures with Applications to Neuroscience
• Multiple Imputation of Missing Covariates in Randomized Controlled Trials
• A Bayesian Strategy to the 20 Question Game with Applications to Recommender Systems
• Applied Factor Dynamic Analysis for Macroeconomic Forecasting
• A Theory of Statistical Inference for Ensuring the Robustness of Scientific Results
• Bayesian Inference Via Partitioning Under Differential Privacy
• A Bayesian Forward Simulation Approach to Establishing a Realistic Prior Model for Complex Geometrical Objects
• Two Applications of Summary Statistics: Integrating Information Across Genes and Confidence Intervals with Missing Data
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Home > FACULTIES > Statistical and Actuarial Sciences > STATS-ETD

Statistics and Actuarial Sciences Theses and Dissertations

This collection contains theses and dissertations from the Department of Statistics and Actuarial Sciences, collected from the Scholarship@Western Electronic Thesis and Dissertation Repository

Theses/Dissertations from 2024 2024

Studies of compound risk models with dependence and parameter uncertainty , Dechen Gao

Theses/Dissertations from 2023 2023

Parameter Estimation for Normally Distributed Grouped Data and Clustering Single-Cell RNA Sequencing Data via the Expectation-Maximization Algorithm , Zahra Aghahosseinalishirazi

Statistical modelling and applications for sustainable-development goals , Yiyang Chen

Multivariate Regression Analysis for Data with Measurement Error, Missing Values, and/or Sparsity Structures , Jingyu Cui

Addressing the Impact of Time-Dependent Social Groupings on Animal Survival and Recapture Rates in Mark-Recapture Studies , Alexandru M. Draghici

Generalized Poisson random variables: Their distributional properties and actuarial applications , Pouya Faroughi

Optimizing Dynamic Treatment Regimes with Q-Learning: Complications due to Error-Prone Data and Applications to COVID-19 Data , Yasin Khadem Charvadeh

Estimating the spatial correlation structure of measurement error in functional magnetic resonance imaging (fMRI) to improve multivariate inference , Lingling Lin

Cyber risk valuation via a hidden Markov-modulated modelling approach , Yuying Li

Advances in Copula Estimation and Distribution Theory , Yishan Zang

Modelling long-term security returns , XINGHAN ZHU

Theses/Dissertations from 2022 2022

Efficiency Improvements in the Least-Squares Monte Carlo Algorithm , François-Michel Boire

Portfolio Optimization Analysis in the Family of 4/2 Stochastic Volatility Models , Yuyang Cheng

Early-Warning Alert Systems for Financial-Instability Detection: An HMM-Driven Approach , Xing Gu

The Analysis of Mark-recapture Data with Individual Heterogeneity via the H-likelihood , Han-na Kim

Statistical Applications to the Management of Intensive Care and Step-down Units , Yawo Mamoua Kobara

Regression-based Methods for Dynamic Treatment Regimes with Mismeasured Covariates or Misclassified Response , Dan Liu

Statistical Roles of the G-expectation Framework in Model Uncertainty: the Semi-G-structure as a Stepping Stone , Yifan Li

Risk theory: data-driven models , Yang Miao

New Developments on the Estimability and the Estimation of Phase-Type Actuarial Models , Cong Nie

Copulas, maximal dependence, and anomaly detection in bi-variate time series , Ning Sun

Interdisciplinary Knowledge Exchange in Statistics with Applications in Fire Science and Statistical Education , Chelsea Uggenti

On the Geometry of Multi-Affine Polynomials , Junquan Xiao

Understanding Deep Learning with Noisy Labels , Li Yi

An Analysis of Weighted Least Squares Monte Carlo , Xiaotian Zhu

Application Of A Polynomial Affine Method In Dynamic Portfolio Choice , Yichen Zhu

Theses/Dissertations from 2021 2021

A class of phase-type ageing models and their lifetime distributions , Boquan Cheng

Application of Stochastic Control to Portfolio Optimization and Energy Finance , Junhe Chen

Making Sense of Noisy Data: Theory and Applications , Lingzhi Chen

The Mean-Reverting 4/2 Stochastic Volatility Model: Properties And Financial Applications , Zhenxian Gong

Compound Sums, Their Distributions, and Actuarial Pricing , Ang Li

On the Estimation of Heston-Nandi GARCH Using Returns and/or Options: A Simulation-based Approach , Xize Ye

Theses/Dissertations from 2020 2020

A Treatise of PD-LGD Correlation Modelling , Wisdom S. Avusuglo WSA

Visualization and Joint Analysis of Monitored Multivariate Spatio-Temporal Data with Applications to Forest Fire Modelling and Sports Analytics , Devan Becker

Generalized 4/2 Factor Model , Yuyang Cheng

Renewable-energy resources, economic growth and their causal link , Yiyang Chen

Some Insurance Options on Stochastic Drawdowns , Filip Dikic

Extensions of Classification Method Based on Quantiles , Yuanhao Lai

Point Process Modelling of Objects in the Star Formation Complexes of the M33 Galaxy , Dayi Li

Classification-based method for estimating dynamic treatment regimes , Junwei Shen

Statistical Methods with a Focus on Joint Outcome Modeling and on Methods for Fire Science , Da Zhong Xi

Ranking comments: An Entropy-based Method with Word Embedding Clustering , Yuyang Zhang

Theses/Dissertations from 2019 2019

A computationally efficient methodology in pricing a guaranteed minimum accumulation benefit , Yiming Huang

Some Recent Developments on Pareto-optimal Reinsurance , Wenjun Jiang

Classification with Measurement Error in Covariates Or Response, with Application to Prostate Cancer Imaging Study , Kexin Luo

Exploring the Estimability of Mark-Recapture Models with Individual, Time-Varying Covariates using the Scaled Logit Link Function , Jiaqi Mu

Split credibility: A two-dimensional semi-linear credibility model , Jingbing Qiu

Advances in Moment-Based Distributional Methodologies , Yishan Zang

How to Rank Answers in Text Mining , Guandong Zhang

On the Sparre-Andersen Risk Models , Ruixi Zhang

Valuation and Risk Management of Some Longevity and P&C Insurance Products , Yixing Zhao

Theses/Dissertations from 2018 2018

Modelling the Common Risk among Equities Using a New Time Series Model , Jingjia Chu

Stochastic modelling of implied correlation index and herd behavior index. Evidence, properties and pricing. , Lin Fang

Optimal Trading of a Storable Commodity via Forward Markets , Behzad Ghafouri

Statistical Modeling of CO2 Flux Data , Fang He

Advances in the Modeling of Heavy-tailed Distributions , Sang Jin Kang

The Statistical Exploration in the $G$-expectation Framework: The Pseudo Simulation and Estimation of Variance Uncertainty , Yifan Li

Statistical tools for assessment of spatial properties of mutations observed under the microarray platform , Bin Luo

Valuation of Multiple Exercise Option Using a Modified Longstaff and Schwartz Approach , Rahim Mohammadhasani Khorasany

Statistical Applications in Healthcare Systems , Maryam Mojalal

Exact Box-Cox Analysis , Samira Soleymani

Anisotropic kernel smoothing for change-point data with an analysis of fire spread rate variability , John Ronald James Thompson

Some applications of higher-order hidden Markov models in the exotic commodity markets , Heng Xiong

Advances in Semi-Nonparametric Density Estimation and Shrinkage Regression , Hossein Zareamoghaddam

Analysis Challenges for High Dimensional Data , Bangxin Zhao

Theses/Dissertations from 2017 2017

Properties of k-isotropic functions , Tianpei Jiang

Data-Adaptive Kernel Support Vector Machine , Xin Liu

Annuity Product Valuation and Risk Measurement under Correlated Financial and Longevity Risks , Soohong Park

Statistical Modelling, Optimal Strategies and Decisions in Two-Period Economies , Jiang Wu

Theses/Dissertations from 2016 2016

Joint Models for Spatial and Spatio-Temporal Point Processes , Alisha Albert-Green

Applications of Credit Scoring Models , Mimi Mei Ling Chong

Joint Analysis of Zero-heavy Longitudinal Outcomes: Models and Comparison of Study Designs , Erin R. Lundy

Data Smoothing Techniques: Historical and Modern , Lori L. Murray

Joint Modelling in Liver Transplantation , Elizabeth M. Renouf

Probability Models for Health Care Operations with Application to Emergency Medicine , Azaz Bin Sharif

Advances in Portmanteau Diagnostic Tests , Jinkun Xiao

Actuarial Modelling with Mixtures of Markov Chains , Yuzhou Zhang

Theses/Dissertations from 2015 2015

Healthy And Unhealthy Statistics: Examining The Impact Of Erroneous Statistical Analyses In Health-Related Research , Britney Allen

Recent Advances in Accumulating Priority Queues , Na Li

Quantitative Techniques for Spread Trading in Commodity Markets , Mir Hashem Moosavi Avonleghi

A Novel Method for Assessing Co-monotonicity: an Interplay between Mathematics and Statistics with Applications , Danang T. Qoyyimi

Completely monotone and Bernstein functions with convexity properties on their measures , Shen Shan

Online Nonparametric Estimation of Stochastic Differential Equations , Xin Wang

On the Dual Risk Models , Chen Yang

Theses/Dissertations from 2014 2014

Statistical methods for the analysis of RNA sequencing data , Man-Kee Maggie Chu

Valuation and Risk Measurement of Guaranteed Annuity Options under Stochastic Environment , Huan Gao

Statistical Applications in Wildfire Management and Prediction , Lengyi Han

Computing and Approximation Methods for the Distribution of Multivariate Aggregate Claims , Tao Jin

The Doubly Adaptive LASSO Methods for Time Series Analysis , Zi Zhen Liu

Risk models with dependence and perturbation , Zhong Li

Censored Time Series Analysis , Nagham Muslim Mohammad

A Spatial Analysis of Forest Fire Survival and a Marked Cluster Process for Simulating Fire Load , Amy A. Morin

Estimation of Hidden Markov Models and Their Applications in Finance , Anton Tenyakov

Perfect and Nearly Perfect Sampling of Work-conserving Queues , Yaofei Xiong

Decision Theory Based Models in Insurance and Beyond , Raymond Ye Zhang

Theses/Dissertations from 2013 2013

Seasonal Decomposition for Geographical Time Series using Nonparametric Regression , Hyukjun Gweon

Stochastic simulation and spatial statistics of large datasets using parallel computing , Jonathan SW Lee

Flexible Partially Linear Single Index Regression Models for Multivariate Survival Data , Na Lei

Joint outcome modeling using shared frailties with application to temporal streamflow data , Lihua Li

Asymptotic Theory for GARCH-in-mean Models , Weiwei Liu

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School of Mathematics & Statistics

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• Statistics Thesis Topics
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Statistics thesis topics

Below are sample topics available for prospective postgraduate research students. These sample topics do not contain every possible project; they are aimed at giving an impression of the breadth of different topics available. Most prospective supervisors would be more than happy to discuss projects not listed below.

Funded projects are projects with project-specific funding. Funding for other projects is usally available on a competitive basis.

Modelling in Space and Time - Example Research Projects

Information about postgraduate research opportunities and how to apply can be found on the  Postgraduate Research Study page . Below is a selection of projects that could be undertaken with our group.

Evaluating probabilistic forecasts in high-dimensional settings (PhD)

Supervisors:   Jethro Browell Relevant research groups:  Modelling in Space and Time , Computational Statistics , Applied Probability and Stochastic Processes

Many decisions are informed by forecasts, and almost all forecasts are uncertain to some degree. Probabilistic forecasts quantify uncertainty to help improve decision-making and are playing an important role in fields including weather forecasting, economics, energy, and public policy. Evaluating the quality of past forecasts is essential to give forecasters and forecast users confidence in their current predictions, and to compare the performance of forecasting systems.

While the principles of probabilistic forecast evaluation have been established over the past 15 years, most notably that of “ sharpness subject to calibration/reliability” , we lack a complete toolkit for applying these principles in many situations, especially those that arise in high-dimensional settings. Furthermore, forecast evaluation must be interpretable by forecast users as well as expert forecasts, and assigning value to marginal improvements in forecast quality remains a challenge in many sectors.

This PhD will develop new statistical methods for probabilistic forecast evaluation considering some of the following issues:

• Verifying probabilistic calibration conditional on relevant covariates
• Skill scores for multivariate probabilistic forecasts where “ideal” performance is unknowable
• Assigning value to marginal forecast improvement though the convolution of utility functions and Murphey Diagrams
• Development of the concept of “anticipated verification” and “predicting the of uncertainty of future forecasts”
• Decomposing forecast misspecification (e.g. into spatial and temporal components)
• Evaluation of  Conformal Predictions

Good knowledge of multivariate statistics is essential, prior knowledge of probabilistic forecasting and forecast evaluation would be an advantage.

Adaptive probabilistic forecasting (PhD)

Supervisors:   Jethro Browell Relevant research groups:   Modelling in Space and Time , Computational Statistics , Applied Probability and Stochastic Processes

Data-driven predictive models depend on the representativeness of data used in model selection and estimation. However, many processes change over time meaning that recent data is more representative than old data. In this situation, predictive models should track these changes, which is the aim of “online” or “adaptive” algorithms. Furthermore, many users of forecasts require probabilistic forecasts, which quantify uncertainty, to inform their decision-making. Existing adaptive methods such as Recursive Least Squares, the Kalman Filter have been very successful for adaptive point forecasting, but adaptive probabilistic forecasting has received little attention. This PhD will develop methods for adaptive probabilistic forecasting from a theoretical perspective and with a view to apply these methods to problems in at least one application area to be determined.

In the context of adaptive probabilistic forecasting, this PhD may consider:

• Online estimation of Generalised Additive Models for Location Scale and Shape
• Online/adaptive (multivariate) time series prediction
• Online aggregation (of experts, or hierarchies)

A good knowledge of methods for time series analysis and regression is essential, familiarity with flexible regression (GAMs) and distributional regression (GAMLSS/quantile regression) would be an advantage.

The evolution of shape (PhD)

Supervisors:   Vincent Macaulay Relevant research groups:   Bayesian Modelling and Inference , Modelling in Space and Time , Statistical Modelling for Biology, Genetics and *omics

Shapes of objects change in time. Organisms evolve and in the process change form: humans and chimpanzees derive from some common ancestor presumably different from either in shape. Designed objects are no different: an Art Deco tea pot from the 1920s might share some features with one from Ikea in 2010, but they are different. Mathematical models of evolution for certain data types, like the strings of As, Gs , Cs and Ts in our evolving DNA, are quite mature and allow us to learn about the relationships of the objects (their phylogeny or family tree), about the changes that happen to them in time (the evolutionary process) and about the ways objects were configured in the past (the ancestral states), by statistical techniques like phylogenetic analysis. Such techniques for shape data are still in their infancy. This project will develop novel statistical inference approaches (in a Bayesian context) for complex data objects, like functions, surfaces and shapes, using Gaussian-process models, with potential application in fields as diverse as language evolution, morphometrics and industrial design.

New methods for analysis of migratory navigation (PhD)

Supervisors:   Janine Illian Relevant research groups:   Modelling in Space and Time , Bayesian Modelling and Inference , Computational Statistics , Environmental, Ecological Sciences and Sustainability

Joint project with Dr Urška Demšar (University of St Andrews)

Migratory birds travel annually across vast expanses of oceans and continents to reach their destination with incredible accuracy. How they are able to do this using only locally available cues is still not fully understood. Migratory navigation consists of two processes: birds either identify the direction in which to fly (compass orientation) or the location where they are at a specific moment in time (geographic positioning). One of the possible ways they do this is to use information from the Earth’s magnetic field in the so-called geomagnetic navigation (Mouritsen 2018). While there is substantial evidence (both physiological and behavioural) that they do sense magnetic field (Deutschlander and Beason 2014), we however still do not know exactly which of the components of the field they use for orientation or positioning. We also do not understand how rapid changes in the field affect movement behaviour.

There is a possibility that birds can sense these rapid large changes and that this may affect their navigational process. To study this, we need to link accurate data on Earth’s magnetic field with animal tracking data. This has only become possible very recently through new spatial data science advances:  we developed the MagGeo tool, which links contemporaneous geomagnetic data from Swarm satellites of the European Space Agency with animal tracking data (Benitez Paez et al. 2021).

Linking geomagnetic data to animal tracking data however creates a highly-dimensional data set, which is difficult to explore. Typical analyses of contextual environmental information in ecology include representing contextual variables as co-variates in relatively simple statistical models (Brum Bastos et al. 2021), but this is not sufficient for studying detailed navigational behaviour. This project will analyse complex spatio-temporal data using computationally efficient statistical model fitting approches in a Bayesian context.

This project is fully based on open data to support reproducibility and open science. We will test our new methods by annotating publicly available bird tracking data (e.g. from repositories such as Movebank.org), using the open MagGeo tool and implementing our new methods as Free and Open Source Software (R/Python).

Benitez Paez F, Brum Bastos VdS, Beggan CD, Long JA and Demšar U, 2021. Fusion of wildlife tracking and satellite geomagnetic data for the study of animal migration.  Movement Ecology , 9:31.  https://doi.org/10.1186/s40462-021-00268-4

Brum Bastos VdS, Łos M, Long JA, Nelson T and Demšar U, 2021, Context-aware movement analysis in ecology: a systematic review.  International Journal of Geographic Information Science ,  https://doi.org/10.1080/13658816.2021.1962528

Deutschlander ME and Beason RC, 2014. Avian navigation and geographic positioning.  Journal of Field Ornithology , 85(2):111–133. https://doi.org/10.1111/jofo.12055

Integrated spatio-temporal modelling for environmental data (PhD)

Supervisors:   Janine Illian Relevant research groups:   Modelling in Space and Time ,  Bayesian Modelling and Inference ,  Computational Statistics ,  Environmental, Ecological Sciences and Sustainability

(Jointly supervised by Peter Henrys, CEH)

The last decade has seen a proliferation of environmental data with vast quantities of information available from various sources. This has been due to a number of different factors including: the advent of sensor technologies; the provision of remotely sensed data from both drones and satellites; and the explosion in citizen science initiatives. These data represent a step change in the resolution of available data across space and time - sensors can be streaming data at a resolution of seconds whereas citizen science observations can be in the hundreds of thousands.  

Over the same period, the resources available for traditional field surveys have decreased dramatically whilst logistical issues (such as access to sites, ) have increased. This has severely impacted the ability for field survey campaigns to collect data at high spatial and temporal resolutions. It is exactly this sort of information that is required to fit models that can quantify and predict the spread of invasive species, for example. 

Whilst we have seen an explosion of data across various sources, there is no single source that provides both the spatial and temporal intensity that may be required when fitting complex spatio-temporal models (cf invasive species example) - each has its own advantages and benefits in terms of information content. There is therefore potentially huge benefit in beginning together data from these different sources within a consistent framework to exploit the benefits each offers and to understand processes at unprecedented resolutions/scales that would be impossible to monitor. 

Current approaches to combining data in this way are typically very bespoke and involve complex model structures that are not reusable outside of the particular application area. What is needed is an overarching generic methodological framework and associated software solutions to implement such analyses. Not only would such a framework provide the methodological basis to enable researchers to benefit from this big data revolution, but also the capability to change such analyses from being stand alone research projects in their own right, to more operational, standard analytical routines. 

FInally, such dynamic, integrated analyses could feedback into data collection initiatives to ensure optimal allocation of effort for traditional surveys or optimal power management for sensor networks. The major step change being that this optimal allocation of effort is conditional on other data that is available. So, for example, given the coverage and intensity of the citizen science data, where should we optimally send our paid surveyors? The idea is that information is collected at times and locations that provide the greatest benefit in understanding the underpinning stochastic processes. These two major issues - integrated analyses and adaptive sampling - ensure that environmental monitoring is fit for purpose and scientists, policy and industry can benefit from the big data revolution. 

This project will develop an integrated statistical modelling strategy that provides a single modelling framework for enabling quantification of ecosystem goods and services while accounting for the fundamental differences in different data streams. Data collected at different spatial resolutions can be used within the same model through projecting it into continuous space and projecting it back into the landscape level of interest.  As a result, decisions can be made at the relevant spatial scale and uncertainty is propagated through, facilitating appropriate decision making.

Statistical methodology for assessing the impacts of offshore renewable developments on marine wildlife (PhD)

(jointly supervised by Esther Jones and Adam Butler, BIOSS)

Assessing the impacts of offshore renewable developments on marine wildlife is a critical component of the consenting process. A NERC-funded project, ECOWINGS, will provide a step-change in analysing predator-prey dynamics in the marine environment, collecting data across trophic levels against a backdrop of developing wind farms and climate change. Aerial survey and GPS data from multiple species of seabirds will be collected contemporaneously alongside prey data available over the whole water column from an automated surface vehicle and underwater drone.

These methods of data collection will generate 3D space and time profiles of predators and prey, creating a rich source of information and enormous potential for modelling and interrogation. The data present a unique opportunity for experimental design across a dynamic and changing marine ecosystem, which is heavily influenced by local and global anthropogenic activities. However, these data have complex intrinsic spatio-temporal properties, which are challenging to analyse. Significant statistical methods development could be achieved using this system as a case study, contributing to the scientific knowledge base not only in offshore renewables but more generally in the many circumstances where patchy ecological spatio-temporal data are available. 

This PhD project will develop spatio-temporal modelling methodology that will allow user to anaylse these exciting - and complex - data sets and help inform our knowledge on the impact of off-shore renewable on wildlife. 

Analysis of spatially correlated functional data objects (PhD)

Supervisors:   Surajit Ray Relevant research groups:   Modelling in Space and Time ,  Computational Statistics ,  Nonparametric and Semi-parametric Statistics ,  Imaging, Image Processing and Image Analysis

Historically, functional data analysis techniques have widely been used to analyze traditional time series data, albeit from a different perspective. Of late, FDA techniques are increasingly being used in domains such as environmental science, where the data are spatio-temporal in nature and hence is it typical to consider such data as functional data where the functions are correlated in time or space. An example where modeling the dependencies is crucial is in analyzing remotely sensed data observed over a number of years across the surface of the earth, where each year forms a single functional data object. One might be interested in decomposing the overall variation across space and time and attribute it to covariates of interest. Another interesting class of data with dependence structure consists of weather data on several variables collected from balloons where the domain of the functions is a vertical strip in the atmosphere, and the data are spatially correlated. One of the challenges in such type of data is the problem of missingness, to address which one needs develop appropriate spatial smoothing techniques for spatially dependent functional data. There are also interesting design of experiment issues, as well as questions of data calibration to account for the variability in sensing instruments. Inspite of the research initiative in analyzing dependent functional data there are several unresolved problems, which the student will work on:

• robust statistical models for incorporating temporal and spatial dependencies in functional data
• developing reliable prediction and interpolation techniques for dependent functional data
• developing inferential framework for testing hypotheses related to simplified dependent structures
• analysing sparsely observed functional data by borrowing information from neighbours
• visualisation of data summaries associated with dependent functional data
• Clustering of functional data

Estimating the effects of air pollution on human health (PhD)

Supervisors:   Duncan Lee Relevant research groups:   Modelling in Space and Time ,  Biostatistics, Epidemiology and Health Applications

The health impact of exposure to air pollution is thought to reduce average life expectancy by six months, with an estimated equivalent health cost of 19 billion each year (from DEFRA). These effects have been estimated using statistical models, which quantify the impact on human health of exposure in both the short and the long term. However, the estimation of such effects is challenging, because individual level measures of health and pollution exposure are not available. Therefore, the majority of studies are conducted at the population level, and the resulting inference can only be made about the effects of pollution on overall population health. However, the data used in such studies are spatially misaligned, as the health data relate to extended areas such as cities or electoral wards, while the pollution concentrations are measured at individual locations. Furthermore, pollution monitors are typically located where concentrations are thought to be highest, known as preferential sampling, which is likely to result in overly high measurements being recorded. This project aims to develop statistical methodology to address these problems, and thus provide a less biased estimate of the effects of pollution on health than are currently produced.

Mapping disease risk in space and time (PhD)

Disease risk varies over space and time, due to similar variation in environmental exposures such as air pollution and risk inducing behaviours such as smoking.  Modelling the spatio-temporal pattern in disease risk is known as disease mapping, and the aims are to: quantify the spatial pattern in disease risk to determine the extent of health inequalities,  determine whether there has been any increase or reduction in the risk over time, identify the locations of clusters of areas at elevated risk, and quantify the impact of exposures, such as air pollution, on disease risk. I am working on all these related problems at present, and I have PhD projects in all these areas.

Bayesian Mixture Models for Spatio-Temporal Data (PhD)

Supervisors:   Craig Anderson Relevant research groups:   Modelling in Space and Time , Bayesian Modelling and Inference , Biostatistics, Epidemiology and Health Applications

The prevalence of disease is typically not constant across space – instead the risk tends to vary from one region to another.  Some of this variability may be down to environmental conditions, but many of them are driven by socio-economic differences between regions, with poorer regions tending to have worse health than wealthier regions.  For example, within the the Greater Glasgow and Clyde region, where the World Health Organisation noted that life expectancy ranges from 54 in Calton to 82 in Lenzie, despite these areas being less than 10 miles apart. There is substantial value to health professionals and policymakers in identifying some of the causes behind these localised health inequalities.

Disease mapping is a field of statistical epidemiology which focuses on estimating the patterns of disease risk across a geographical region. The main goal of such mapping is typically to identify regions of high disease risk so that relevant public health interventions can be made. This project involves the development of statistical models which will enhance our understanding regional differences in the risk of suffering from major diseases by focusing on these localised health inequalities.

Standard Bayesian hierarchical models with a conditional autoregressive prior are frequently used for risk estimation in this context, but these models assume a smooth risk surface which is often not appropriate in practice. In reality, it will often be the case that different regions have vastly different risk profiles and require different data generating functions as a result.

In this work we propose a mixture model based approach which allows different sub-populations to be represented by different underlying statistical distributions within a single modelling framework. By integrating CAR models into mixture models, researchers can simultaneously account for spatial dependencies and identify distinct disease patterns within subpopulations.

Bayesian Modelling and Inference - Example Research Projects

Modelling genetic variation (msc/phd).

Supervisors:   Vincent Macaulay Relevant research groups:   Bayesian Modelling and Inference ,  Statistical Modelling for Biology, Genetics and *omics

Variation in the distribution of different DNA sequences across individuals has been shaped by many processes which can be modelled probabilistically, processes such as demographic factors like prehistoric population movements, or natural selection. This project involves developing new techniques for teasing out information on those processes from the wealth of raw data that is now being generated by high-throughput genetic assays, and is likely to involve computationally-intensive sampling techniques to approximate the posterior distribution of parameters of interest. The characterization of the amount of population structure on different geographical scales will influence the design of experiments to identify the genetic variants that increase risk of complex diseases, such as diabetes or heart disease.

The evolution of shape (PhD)

Supervisors:   Vincent Macaulay Relevant research groups:   Bayesian Modelling and Inference ,  Modelling in Space and Time , Statistical Modelling for Biology, Genetics and *omics

New methods for analysis of migratory navigation (PhD)

Integrated spatio-temporal modelling for environmental data (phd), statistical methodology for assessing the impacts of offshore renewable developments on marine wildlife (phd).

This PhD project will develop spatio-temporal modelling methodology that will allow user to anaylse these exciting - and complex - data sets and help inform our knowledge on the impact of off-shore renewable on wildlife.

Bayesian variable selection for genetic and genomic studies (PhD)

Supervisors:   Mayetri Gupta Relevant research groups:   Bayesian Modelling and Inference ,  Computational Statistics ,  Statistical Modelling for Biology, Genetics and *omics

An important issue in high-dimensional regression problems is the accurate and efficient estimation of models when, compared to the number of data points, a substantially larger number of potential predictors are present. Further complications arise with correlated predictors, leading to the breakdown of standard statistical models for inference; and the uncertain definition of the outcome variable, which is often a varying composition of several different observable traits. Examples of such problems arise in many scenarios in genomics- in determining expression patterns of genes that may be responsible for a type of cancer; and in determining which genetic mutations lead to higher risks for occurrence of a disease. This project involves developing broad and improved Bayesian methodologies for efficient inference in high-dimensional regression-type problems with complex multivariate outcomes, with a focus on genetic data applications.

The successful candidate should have a strong background in methodological and applied Statistics, expert skills in relevant statistical software or programming languages (such as R, C/C++/Python), and also have a deep interest in developing knowledge in cross-disciplinary topics in genomics. The candidate will be expected to consolidate and master an extensive range of topics in modern Statistical theory and applications during their PhD, including advanced Bayesian modelling and computation, latent variable models, machine learning, and methods for Big Data. The successful candidate will be considered for funding to cover domestic tuition fees, as well as paying a stipend at the Research Council rate for four years.

Bayesian statistical data integration of single-cell and bulk “OMICS” datasets with clinical parameters for accurate prediction of treatment outcomes in Rheumatoid Arthritis (PhD)

Supervisors:   Mayetri Gupta Relevant research groups:   Bayesian Modelling and Inference ,  Computational Statistics ,  Statistical Modelling for Biology, Genetics and *omics ,  Biostatistics, Epidemiology and Health Applications

In recent years, many different computational methods to analyse biological data have been established: including DNA (Genomics), RNA (Transcriptomics), Proteins (proteomics) and Metabolomics, that captures more dynamic events. These methods were refined by the advent of single cell technology, where it is now possible to capture the transcriptomics profile of single cells, spatial arrangements of cells from flow methods or imaging methods like functional magnetic resonance imaging. At the same time, these OMICS data can be complemented with clinical data – measurement of patients, like age, smoking status, phenotype of disease or drug treatment. It is an interesting and important open statistical question how to combine data from different “modalities” (like transcriptome with clinical data or imaging data) in a statistically valid way, to compare different datasets and make justifiable statistical inferences. This PhD project will be jointly supervised with  Dr. Thomas Otto  and  Prof. Stefan Siebert  from the  Institute of Infection, Immunity & Inflammation ), you will explore how to combine different datasets using Bayesian latent variable modelling, focusing on clinical datasets from Rheumatoid Arthritis.

Funding Notes

The successful candidate will be considered for funding to cover domestic tuition fees, as well as paying a stipend at the Research Council rate for four years.

Scalable Bayesian models for inferring evolutionary traits of plants (PhD)

Supervisors:   Vinny Davies ,  Richard Reeve Relevant research groups:   Bayesian Modelling and Inference ,  Computational Statistics ,  Environmental, Ecological Sciences and Sustainability ,  Statistical Modelling for Biology, Genetics and *omics

The functional traits and environmental preferences of plant species determine how they will react to changes resulting from global warming. The main global biodiversity repositories, such as the Global Biodiversity Information Facility ( GBIF ), contain hundreds of millions of records from hundreds of thousands of species in the plant kingdom alone, and the spatiotemporal data in these records can be associated with soil, climate or other environmental data from other databases. Combining these records allow us to identify environmental preferences, especially for common species where many records exist. Furthermore, in a previous PhD studentship we showed that these traits are highly evolutionarily conserved ( Harris et al., 2022 ), so it is possible to impute the preferences for rare species where little data exists using phylogenetic inference techniques.

The aim of this PhD project is to investigate the application of Bayesian variable selection methods to identify these evolutionarily conserved traits more effectively, and to quantify these traits and their associated uncertainty for all plant species for use in a plant ecosystem digital twin that we are developing separately to forecast the impact of climate change on biodiversity. In another PhD studentship, we previously developed similar methods for trait inference in viral evolution ( Davies et al., 2017 ;  Davies et al., 2019 ), but due to the scale of the data here, these methods will need to be significantly enhanced. We therefore propose a project to investigate extensions to methods for phylogenetic trait inference to handle datasets involving hundreds of millions of records in phylogenies with hundreds of thousands of tips, potentially through either sub-sampling ( Quiroz et al, 2018 ) or modelling splitting and recombination ( Nemeth & Sherlock, 2018 ).

Computational Statistics - Example Research Projects

Supervisors:   Jethro Browell Relevant research groups:  Modelling in Space and Time ,  Computational Statistics ,  Applied Probability and Stochastic Processes

Supervisors:   Jethro Browell Relevant research groups:   Modelling in Space and Time ,  Computational Statistics ,  Applied Probability and Stochastic Processes

This project will develop an integrated statistical modelling strategy that provides a single modelling framework for enabling quantification of ecosystem goods and services while accounting for the fundamental differences in different data streams. Data collected at different spatial resolutions can be used within the same model through projecting it into continuous space and projecting it back into the landscape level of interest.  As a result, decisions can be made at the relevant spatial scale and uncertainty is propagated through, facilitating appropriate decision making. 

Statistical methodology for assessing the impacts of offshore renewable developments on marine wildlife (PhD)

Bayesian variable selection for genetic and genomic studies (phd), bayesian statistical data integration of single-cell and bulk “omics” datasets with clinical parameters for accurate prediction of treatment outcomes in rheumatoid arthritis (phd), scalable bayesian models for inferring evolutionary traits of plants (phd).

The aim of this PhD project is to investigate the application of Bayesian variable selection methods to identify these evolutionarily conserved traits more effectively, and to quantify these traits and their associated uncertainty for all plant species for use in a plant ecosystem digital twin that we are developing separately to forecast the impact of climate change on biodiversity. In another PhD studentship, we previously developed similar methods for trait inference in viral evolution ( Davies et al., 2017 ;  Davies et al., 2019 ), but due to the scale of the data here, these methods will need to be significantly enhanced. We therefore propose a project to investigate extensions to methods for phylogenetic trait inference to handle datasets involving hundreds of millions of records in phylogenies with hundreds of thousands of tips, potentially through either sub-sampling ( Quiroz et al, 2018 ) or modelling splitting and recombination ( Nemeth & Sherlock, 2018 ).

Multi objective Bayesian optimisation for in silico  to real metabolomics experiments    (PhD/MSc)

Supervisors:   Vinny Davies ,  Craig Alexander Relevant research groups:   Computational Statistics ,  Machine Learning and AI ,  Emulation and Uncertainty Quantification ,  Statistical Modelling for Biology, Genetics and *omics ,  Statistics in Chemistry/Physics

Untargeted metabolomics experiments aim to  identify  the small molecules that make up a particular sample  (e.g. ,  blood), allowing   us to  identify  biomarkers, discover new chemicals, or understand the  metabolism  ( Smith et al., 2014 ) .  Data Dependent Acquisition  (DDA)  methods  are used to collect  the information needed to  identify  the metabolites ,  and various more advanced  DDA  methods have  recently  been designed to improve this process  ( Davies et al. (2021) ;  McBride et al. (2023) ) . Each of  these methods , however,  ha s  parameters that must be  chosen   in order to  maximise the amount of relevant data  (metabolite spectra)  that is collected . Our recent work  led to the design of  a Virtual Metabolomics Mass Spectrometer ( ViMMS ) in which we can run  computer simulations of experiments  and test different parameter  settings  ( Wandy et al., 2019 ,  2022 ). Previously this has involve d  running a  pre-determined set of parameters as part of a grid search  in  ViMMS ,  and then choosing the best parameter settings  based on a single measure of performance. The proposed  M . Res .  (or Ph . D . ) will  extend this appro ach by using  multi objective  Bayesian Optimisation  to  adapt simulations and optimise over  multiple  different  measurements of quality . By  optimising parameters in this  manner,  we can help improve real experiments currently underway at the University of Glasgow and beyond.

Analysis of spatially correlated functional data objects (PhD)

Nonparametric and semi-parametric statistics - example research projects, modality of mixtures of distributions (phd).

Supervisors:   Surajit Ray Relevant research groups:   Nonparametric and Semi-parametric Statistics ,  Applied Probability and Stochastic Processes ,  Statistical Modelling for Biology, Genetics and *omics ,  Biostatistics, Epidemiology and Health Applications

Finite mixtures provide a flexible and powerful tool for fitting univariate and multivariate distributions that cannot be captured by standard statistical distributions. In particular, multivariate mixtures have been widely used to perform modeling and cluster analysis of high-dimensional data in a wide range of applications. Modes of mixture densities have been used with great success for organizing mixture components into homogenous groups. But the results are limited to normal mixtures. Beyond the clustering application existing research in this area has provided fundamental results regarding the upper bound of the number of modes, but they too are limited to normal mixtures. In this project, we wish to explore the modality of non-normal distributions and their application to real life problems.

Applied Probability and Stochastic Processes - Example Research Projects

Modality of mixtures of distributions (phd).

Finite mixtures provide a flexible and powerful tool for fitting univariate and multivariate distributions that cannot be captured by standard statistical distributions. In particular, multivariate mixtures have been widely used to perform modeling and cluster analysis of high-dimensional data in a wide range of applications. Modes of mixture densities have been used with great success for organizing mixture components into homogenous groups. But the results are limited to normal mixtures. Beyond the clustering application existing research in this area has provided fundamental results regarding the upper bound of the number of modes, but they too are limited to normal mixtures. In this project, we wish to explore the modality of non-normal distributions and their application to real life problems.

Machine Learning and AI - Example Research Projects

Estimating false discovery rates in metabolite identification using generative ai  (phd).

Supervisors:   Vinny Davies , Andrew Elliott ,  Justin J.J. van der Hooft (Wageningen University) Relevant research groups:   Machine Learning and AI ,  Emulation and Uncertainty Quantification ,  Statistical Modelling for Biology, Genetics and *omics ,  Statistics in Chemistry/Physics

Metabolomics is the study field that aims to map all molecules that are part of an organism, which can help us understand its metabolism and how it can be affected by disease, stress, age, or other factors. During metabolomics experiments, mass spectra of the metabolites are collected and then annotated by comparison against spectral databases such as METLIN ( Smith et al., 2005 ) or GNPS ( Wang et al., 2016 ). Generally, however, these spectral databases do not contain the mass spectra of a large proportion of metabolites, so the best matching spectrum from the database is not always the correct identification. Matches can be scored using cosine similarity, or more advanced methods such as Spec2Vec ( Huber et al., 2021 ), but these scores do not provide any statement about the statistical accuracy of the match. Creating decoy spectral libraries, specifically a large database of fake spectra, is one potential way of estimating False Discovery Rates (FDRs), allowing us to quantify the probability of a spectrum match being correct ( Scheubert et al., 2017 ). However, these methods are not widely used, suggesting there is significant scope to improve their performance and ease of use. In this project, we will use the code framework from our recently developed Virtual Metabolomics Mass Spectrometer (ViMMS) ( Wandy et al., 2019 ,  2022 ) to systematically evaluate existing methods and identify possible improvements. We will then explore how we can use generative AI, e.g., Generative Adversarial Networks or Variational Autoencoders, to train a deep neural network that can create more realistic decoy spectra, and thus improve our estimation of FDRs.

Medical image segmentation and uncertainty quantification (PhD)

Supervisors:  Surajit Ray Relevant research groups:   Machine Learning and AI ,  Imaging, Image Processing and Image Analysis

This project focuses on the application of medical imaging and uncertainty quantification for the detection of tumours. The project aims to provide clinicians with accurate, non-invasive methods for detecting and classifying the presence of malignant and benign tumours. It seeks to combine advanced medical imaging technologies such as ultrasound, computed tomography (CT) and magnetic resonance imaging (MRI) with the latest artificial intelligence algorithms. These methods will automate the detection process and may be used for determining malignancy with a high degree of accuracy. Uncertainty quantification (UQ) techniques will help generate a more precise prediction for tumour malignancy by providing a characterisation of the degree of uncertainty associated with the diagnosis. The combination of medical imaging and UQ will significantly decrease the requirement for performing invasive medical procedures such as biopsies. This will improve the accuracy of the tumour detection process and reduce the duration of diagnosis. The project will also benefit from the development of novel image processing algorithms (e.g. deep learning) and machine learning models. These algorithms and models will help improve the accuracy of the tumour detection process and assist clinicians in making the best treatment decisions.

Generating deep fake left ventricles: a step towards personalised heart treatments (PhD)

Supervisors:  Andrew Elliott , Vinny Davies , Hao Gao Relevant research groups:  Machine Learning and AI , Emulation and Uncertainty Quantification , Biostatistics, Epidemiology and Health Applications , Imaging, Image Processing and Image Analysis

Personalised medicine is an exciting avenue in the field of cardiac healthcare where an understanding of patient-specific mechanisms can lead to improved treatments ( Gao et al., 2017 ). The use of mathematical models to link the underlying properties of the heart with cardiac imaging offers the possibility of obtaining important parameters of heart function non-invasively ( Gao et al., 2015 ). Unfortunately, current estimation methods rely on complex mathematical forward simulations, resulting in a solution taking hours, a time frame not suitable for real-time treatment decisions. To increase the applicability of these methods, statistical emulation methods have been proposed as an efficient way of estimating the parameters ( Davies et al., 2019 ;  Noè et al., 2019 ). In this approach, simulations of the mathematical model are run in advance and then machine learning based methods are used to estimate the relationship between the cardiac imaging and the parameters of interest. These methods are, however, limited by our ability to understand the how cardiac geometry varies across patients which is in term limited by the amount of data available ( Romaszko et al., 2019 ). In this project we will look at AI based methods for generating fake cardiac geometries which can be used to increase the amount of data ( Qiao et al., 2023 ). We will explore different types of AI generation, including Generative Adversarial Networks or Variational Autoencoders, to understand how we can generate better 3D and 4D models of the fake left ventricles and create an improved emulation strategy that can make use of them.

Emulation and Uncertainty Quantification - Example Research Projects

Metabolomics is the study field that aims to map all molecules that are part of an organism, which can help us understand its metabolism and how it can be affected by disease, stress, age, or other factors. During metabolomics experiments, mass spectra of the metabolites are collected and then annotated by comparison against spectral databases such as METLIN ( Smith et al., 2005 ) or GNPS ( Wang et al., 2016 ). Generally, however, these spectral databases do not contain the mass spectra of a large proportion of metabolites, so the best matching spectrum from the database is not always the correct identification. Matches can be scored using cosine similarity, or more advanced methods such as Spec2Vec ( Huber et al., 2021 ), but these scores do not provide any statement about the statistical accuracy of the match. Creating decoy spectral libraries, specifically a large database of fake spectra, is one potential way of estimating False Discovery Rates (FDRs), allowing us to quantify the probability of a spectrum match being correct ( Scheubert et al., 2017 ). However, these methods are not widely used, suggesting there is significant scope to improve their performance and ease of use. In this project, we will use the code framework from our recently developed Virtual Metabolomics Mass Spectrometer (ViMMS) ( Wandy et al., 2019 ,  2022 ) to systematically evaluate existing methods and identify possible improvements. We will then explore how we can use generative AI, e.g., Generative Adversarial Networks or Variational Autoencoders, to train a deep neural network that can create more realistic decoy spectra, and thus improve our estimation of FDRs.

Supervisors: Andrew Elliott , Vinny Davies , Hao Gao Relevant research groups:  Machine Learning and AI ,  Emulation and Uncertainty Quantification ,  Biostatistics, Epidemiology and Health Applications ,  Imaging, Image Processing and Image Analysis

Environmental, Ecological Sciences and Sustainability - Example Research Projects

Statistical methodology for assessing the impacts of offshore renewable developments on marine wildlife (phd), statistical modelling for biology, genetics and *omics - example research projects, modelling genetic variation (msc/phd).

Supervisors:   Vincent Macaulay Relevant research groups:   Bayesian Modelling and Inference ,  Modelling in Space and Time ,  Statistical Modelling for Biology, Genetics and *omics

Bayesian statistical data integration of single-cell and bulk “OMICS” datasets with clinical parameters for accurate prediction of treatment outcomes in Rheumatoid Arthritis (PhD)

Supervisors:   Vinny Davies ,  Richard Reeve ,  Claire Harris (BIOSS) Relevant research groups:   Bayesian Modelling and Inference ,  Computational Statistics ,  Environmental, Ecological Sciences and Sustainability ,  Statistical Modelling for Biology, Genetics and *omics

Supervisors:   Vinny Davies , Andrew Elliott ,  Justin J.J. van der Hooft (Wageningen University) Relevant research groups:   Machine Learning and AI ,  Emulation and Uncertainty Quantification ,  Statistical Modelling for Biology, Genetics and *omics , Statistics in Chemistry/Physics

Multi objective Bayesian optimisation for in silico  to real metabolomics experiments  (PhD/MSc)

Finite mixtures provide a flexible and powerful tool for fitting univariate and multivariate distributions that cannot be captured by standard statistical distributions. In particular, multivariate mixtures have been widely used to perform modeling and cluster analysis of high-dimensional data in a wide range of applications. Modes of mixture densities have been used with great success for organizing mixture components into homogenous groups. But the results are limited to normal mixtures. Beyond the clustering application existing research in this area has provided fundamental results regarding the upper bound of the number of modes, but they too are limited to normal mixtures. In this project, we wish to explore the modality of non-normal distributions and their application to real life problems

Implementing a biology-empowered statistical framework to detect rare varient risk factors for complex diseases in whole genome sequence cohorts (PhD)

Supervisors:   Vincent Macaulay , Luísa Pereira (Geneticist, i3s ) Relevant research groups:  Statistical Modelling for Biology, Genetics and *omics ,  Biostatistics, Epidemiology and Health Applications

The traditional genome-wide association studies to detect candidate genetic risk factors for complex diseases/phenotypes (GWAS) recur largely to the microarray technology, genotyping at once thousands or millions of variants regularly spaced across the genome. These microarrays include mostly common variants (minor allele frequency, MAF>5%), missing candidate rare variants which are the more likely to be deleterious [ 1 ]. Currently, the best strategy to genotype low-frequency (1%<MAF<5%) and rare (MAF<1%) variants is through next generation sequencing, and the increasingly availability of whole genome sequences (WGS) places us in the brink of detecting rare variants associated with complex diseases [ 2 ]. Statistically, this detection constitutes a challenge, as the massive number of rare variants in genomes (for example, 64.7M in 150 Iberian WGSs) would imply genotyping millions/billions of individuals to attain statistical power. In the last couple years, several statistical methods have being tested in the context of association of rare variants with complex traits [ 2 , 3 , 4 ], largely testing strategies to aggregate the rare variants. These works have not yet tested the statistical empowerment that can be gained by incorporating reliable biological evidence on the aggregation of rare variants in the most probable functional regions, such as non-coding regulatory regions that control the expression of genes [ 4 ]. In fact, it has been demonstrated that even for common candidate variants, most of these variants (around 88%; [ 5 ]) are located in non-coding regions. If this is true for the common variants detected by the traditional GWAS, it is highly probable to be also true for rare variants.

In this work, we will implement a biology-empowered statistical framework to detect rare variant risk factors for complex diseases in WGS cohorts. We will recur to the 200,000 WGSs from UK Biobank database [ 6 ], that will be available to scientists before the end of 2023. Access to clinical information of these >40 years old UK residents is also provided. We will build our framework around type-2 diabetes (T2D), a common complex disease for which thousands of common variant candidates have been found [ 7 ]. Also, the mapping of regulatory elements is well known for the pancreatic beta cells that play a leading role in T2D [ 8 ]. We will use this mapping in guiding the rare variants’ aggregation and test it against a random aggregation across the genome. Of course, the framework rationale will be appliable to any other complex disease. We will browse literature for aggregation methods available at the beginning of this work, but we already selected the method SKAT (sequence kernel association test; [ 3 ]) to be tested. SKAT fits a random-effects model to the set of variants within a genomic interval or biologically-meaningful region (such as a coding or regulatory region) and computes variant-set level p-values, while permitting correction for covariates (such as the principal components mentioned above that can account for population stratification between cases and controls).

Biostatistics, Epidemiology and Health Applications - Example Research Projects

Bayesian statistical data integration of single-cell and bulk “omics” datasets with clinical parameters for accurate prediction of treatment outcomes in rheumatoid arthritis (phd).

Supervisors:   Mayetri Gupta Relevant research groups:   Bayesian Modelling and Inference ,  Computational Statistics ,  Vincent Macaulay ,  Biostatistics, Epidemiology and Health Applications

Supervisors: Andrew Elliott , Vinny Davies , Hao Gao Relevant research groups:  Machine Learning and AI ,  Emulation and Uncertainty Quantification ,  Biostatistics, Epidemiology and Health Applications ,  Statistical Modelling for Biology, Genetics and *omics

Supervisors:   Craig Anderson Relevant research groups: Modelling in Space and Time , Bayesian Modelling and Inference , Biostatistics, Epidemiology and Health Applications

Implementing a biology-empowered statistical framework to detect rare varient risk factors for complex diseases in whole genome sequence cohorts (PhD)

Supervisors:   Vincent Macaulay , Luísa Pereira (Geneticist,  i3s ) Relevant research groups:  Statistical Modelling for Biology, Genetics and *omics ,  Biostatistics, Epidemiology and Health Applications

The traditional genome-wide association studies to detect candidate genetic risk factors for complex diseases/phenotypes (GWAS) recur largely to the microarray technology, genotyping at once thousands or millions of variants regularly spaced across the genome. These microarrays include mostly common variants (minor allele frequency, MAF>5%), missing candidate rare variants which are the more likely to be deleterious [ 1 ]. Currently, the best strategy to genotype low-frequency (1%<MAF<5%) and rare (MAF<1%) variants is through next generation sequencing, and the increasingly availability of whole genome sequences (WGS) places us in the brink of detecting rare variants associated with complex diseases [ 2 ]. Statistically, this detection constitutes a challenge, as the massive number of rare variants in genomes (for example, 64.7M in 150 Iberian WGSs) would imply genotyping millions/billions of individuals to attain statistical power. In the last couple years, several statistical methods have being tested in the context of association of rare variants with complex traits [ 2 ,  3 ,  4 ], largely testing strategies to aggregate the rare variants. These works have not yet tested the statistical empowerment that can be gained by incorporating reliable biological evidence on the aggregation of rare variants in the most probable functional regions, such as non-coding regulatory regions that control the expression of genes [ 4 ]. In fact, it has been demonstrated that even for common candidate variants, most of these variants (around 88%; [ 5 ]) are located in non-coding regions. If this is true for the common variants detected by the traditional GWAS, it is highly probable to be also true for rare variants.

Social and Urban Studies - Example Research Projects

Our group has an active PhD student community, and every year we admit new PhD students. We welcome applications from across the world. Further information can be found here .

Imaging, Image Processing and Image Analysis - Example Research Projects

Supervisors:  Andrew Elliott , Vinny Davies , Hao Gao Relevant research groups:  Machine Learning and AI ,  Emulation and Uncertainty Quantification ,  Biostatistics, Epidemiology and Health Applications ,  Imaging, Image Processing and Image Analysis

Statistics in Chemistry/Physics - Example Research Projects

Statistics and data analytics education - example research projects.

Our group has an active PhD student community, and every year we admit new PhD students. We welcome applications from across the world. Further information can be found here .

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Dissertations & Theses

The following is a list of recent statistics and biostatistics PhD Dissertations and Masters Theses.

Jeffrey Gory (2017) PhD Dissertation (Statistics): Marginally Interpretable Generalized Linear Mixed Models Advisors: Peter Craigmile & Steven MacEachern

Yi Lu (2017) PhD Dissertation (Statistics): Function Registration from a Bayesian Perspective Advisors: Radu Herbei & Sebastian Kurtek

Michael Matthews (2017) PhD Dissertation (Statistics):  Extending Ranked Sampling in Inferential Procedures Advisor: Douglas Wolfe

Anna Smith (2017) PhD Dissertation (Statistics):  Statistical Methodology for Multiple Networks Advisor: Catherine Calder

Weiyi Xie (2017) PhD Dissertation (Statistics): A Geometric Approach to Visualization of Variability in Univariate and Multivariate Functional Data Advisor: Sebastian Kurtek

Jingying Zeng (2017) Masters Thesis (Statistics): Latent Factor Models for Recommender Systems and Market Segmentation Through Clustering Advisors: Matthew Pratola & Laura Kubatko

Han Zhang (2017) PhD Dissertation (Statistics): Detecting Rare Haplotype-Environmental Interaction and Nonlinear Effects of Rare Haplotypes using Bayesian LASSO on Quantitative Traits Advisor: Shili Lin

Mark Burch (2016) PhD Dissertation (Biostatistics): Statistical Methods for Network Epidemic Models Advisor: Grzegorz Rempala

Po-hsu Chen (2016) PhD Dissertation (Statistics):  Modeling Multivariate Simulator Outputs with Applications to Prediction and Sequential Pareto Minimization Advisors: Thomas Santner & Angela Dean

Yanan Jia (2016) PhD Dissertation (Statistics): Generalized Bilinear Mixed-Effects Models for Multi-Indexed Multivariate Data Advisor: Catherine Calder

Rong Lu (2016) PhD Dissertation (Biostatistics): Statistical Methods for Functional Genomics Studies Using Observational Data Advisor: Grzegorz Rempala (Public Health)

Junyan Wang (2016) PhD Dissertation (Statistics): Empirical Bayes Model Averaging in the Presence of Model Misfit Advisors: Mario Peruggia & Christopher Hans

Ran Wei (2016) PhD Dissertation (Statistics):  On Estimation Problems in Network Sampling Advisors: David Sivakoff & Elizabeth Stasny

Hui Yang (2016) PhD Dissertation (Statistics):  Adjusting for Bounding and Time-in-Sample Eects in the National Crime Victimization Survey (NCVS) Property Crime Rate Estimation Advisors: Elizabeth Stasny & Asuman Turkmen

Matthew Brems (2015) Masters Thesis (Statistis): The Rare Disease Assumption: The Good, The Bad, and The Ugly Advisor: Shili Lin

Linchao Chen (2015) PhD Dissertation (Statistics):  Predictive Modeling of Spatio-Temporal Datasets in High Dimensions Advisors: Mark Berliner & Christopher Hans

Casey Davis (2015) PhD Dissertation (Statistics):  A Bayesian Approach to Prediction and Variable Selection Using Nonstationary Gaussian Processes Advisors: Christopher Hans & Thomas Santner

Victor Gendre (2015) Masters Thesis (Statistics): Predicting short term exchange rates with Bayesian autoregressive state space models: an investigation of the Metropolis Hastings algorithm forecasting efficiency Advisor: Radu Herbei

Zhengyu Hu (2015) PhD Dissertation (Statistics):  Initializing the EM Algorithm for Data Clustering and Sub-population Detection Advisors: Steven MacEachern & Joseph Verducci

David Kline (2015) PhD Dissertation (Biostatistics): Systematically Missing Subject-Level Data in Longitudinal Research Synthesis Advisors: Eloise Kaizar, Rebecca Andridge (Public Health)

Andrew Landgraf (2015) PhD Dissertation (Statistics): Generalized Principal Component Analysis: Dimensionality Reduction through the Projection of Natural Parameters Advisor: Yoonkyung Lee

Andrew Olsen (2015) PhD Dissertation (Statistics):  When Infinity is Too Long to Wait: On the Convergence of Markov Chain Monte Carlo Methods Advisor: Radu Herbei

Elizabeth   Petraglia (2015) PhD Dissertation (Statistics):  Estimating County-Level Aggravated Assault Rates by Combining Data from the National Crime Victimization Survey (NCVS) and the National Incident-Based Reporting System (NIBRS) Advisor: Elizabeth Stasny

Mark   Risser (2015) PhD Dissertation (Statistics):  Spatially-Varying Covariance Functions for Nonstationary Spatial Process Modeling Advisor: Catherine Calder

John Stettler (2015) PhD Dissertation (Statistics):  The Discrete Threshold Regression Model Advisor: Mario Peruggia

Zachary   Thomas (2015) PhD Dissertation (Statistics):  Bayesian Hierarchical Space-Time Clustering Methods Advisor: Mark Berliner

Sivaranjani   Vaidyanathan (2015) PhD Dissertation (Statistics):  Bayesian Models for Computer Model Calibration and Prediction Advisor: Mark Berliner

Xiaomu Wang (2015) PhD Dissertation (Statistics): Robust Bayes in Hierarchical Modeling and Empirical Bayes Analysis in Multivariate Estimation Advisor: Mark Berliner

Staci White (2015) PhD Dissertation (Statistics):  Quantifying Model Error in Bayesian Parameter Estimation Advisor: Radu Herbei

Jiaqi Zaetz (2015) PhD Dissertation (Statistics): A Riemannian Framework for Shape Analysis of Annotated 3D Objects Advisor: Sebastian Kurtek

Fangyuan Zhang (2015) PhD Dissertation (Biostatistics): Detecting genomic imprinting and maternal effects in family-based association studies Advisor: Shili Lin

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The Role of Statistical Analysis in Master’s Dissertations

Home » Videos » The Role of Statistical Analysis in Master’s Dissertations

When students start working on their Master’s dissertation, they become researchers and are expected to learn more about their field of study and make new contributions to it. The most important part of this academic path is the statistical analysis. Through this piece, we will talk about how important statistics are in Master’s dissertations.

The Link Between Theories and Real Life

Statistical analysis is the link between the theoretical theories put forward in the dissertation and data from the real world. It proves or disproves these hypotheses, which turns the study into more than just a theory.

Why statistical analysis is important for students?

Statistics is an indispensable tool for Master’s students, playing a crucial role in their academic journey. With the advent of custom dissertation writing services , it’s become even more imperative for students to grasp the fundamentals of statistics. A solid foundation in statistics empowers students to critically evaluate the quality of the statistical analyses performed by such services, ensuring that the research presented in their dissertations is both accurate and reliable. Furthermore, mastering statistics equips students with the skills to communicate their research effectively, making their custom dissertations stand out as rigorously researched and well-founded contributions to their fields of study.

Because custom dissertation writing services have become more popular in academia, it is important for Master’s students to have a good understanding of numbers. Statistics is the key to getting the most out of research. It makes sure that the results shown in custom papers are not only reliable but also have an effect. It becomes clear to students as they move through the complicated world of academia how important statistics are for helping them make smart choices, test their hypotheses, and communicate their research clearly, which eventually leads to academic success.

Tools and software for statistics

Different statistical software and tools can be used by master’s students to help them with their study. Here are some of the most popular ones:

The Statistical Package for the Social Sciences (SPSS) is easy to use and is commonly used to look at data in the social sciences and other areas.

The computer language and environment R is free and open source. It works great for statistical computing and graphics.

 Excel

A tool that many people have access to, Microsoft Excel, can also be used for simple statistical research.

Precision and Accuracy

Statistics make sure that study results are precise and correct. They help experts come to objective conclusions, which lowers the chance of mistakes and makes the results more reliable.

Evidence-Based Decision Making

Statistical analysis gives us real-world proof that helps us make decisions. It helps researchers and students make smart decisions by letting them rely on data-driven insights instead of gut feelings or anecdotal proof.

Importance of Statistics in Research

 foundation of research design.

Statistics are the building blocks of study design. Statistics play a big role in shaping the study’s methodology, from choosing the right research methods to figuring out the sample number.

Data Collection and Measurement

Statistics help us gather facts and figure out how to measure things. They help pick the best ways and tools to collect data, which makes sure that the data is useful and accurate.

Data Analysis

The most important part of statistical research is figuring out how to take and use data. In this step, methods such as regression analysis, hypothesis testing, and data modeling are used to find the data’s secret insights.

How Important is Statistics in Master’s Dissertations?

Validating research hypotheses.

In a Master’s dissertation, the researcher comes up with a list of possible outcomes. To prove or disprove these hypotheses, statistical analysis is used. This gives the study more weight.

Drawing Inferences

Researchers can draw conclusions from their data with the help of statistical analysis. The study results can be used for more than just the sample that was studied because these conclusions can be applied to a larger group of people.

Generalizability of Findings

In academia, it’s very important that study results can be used by other people. Stats help us make claims about a whole group based on a small sample, which makes the study more useful and important.

What Statistics Do to Shape Research

Statistics that describe.

You can summarize and show data in a useful way with descriptive statistics. This uses methods like mean, median, and mode to give a big picture of the data.

Stats for Drawing Conclusions

Researchers can make predictions and test theories with the help of inferential statistics, which look into the patterns and relationships in data.

How to Present Statistics in a Clear Way

Lists and charts.

It’s an art in and of itself to show statistical results in a clear way. Data that is hard to understand can be made easier to read with the help of charts and graphs.

How to Read Statistical Results

To share study results, you need to be able to interpret statistical outputs. In this step, you’ll discuss what the statistical results mean and what they mean for the future.

Getting Past Statistical Problems

Figure out the sample size.

A very important part of study design is choosing the right sample size. Statistics help make sure that the sample really does reflect the whole community.

Cleaning up data

That data can be a mess. Statistics gives us ways to clean up data, which makes sure that the study data we use is accurate.

Assumptions about Statistics

For study to be valid, it is important to understand and test statistical assumptions. For students to do correct analyses, they need to be aware of these assumptions.

What a Statistician Does?

Working together with experts.

Working together with analysts or other experts in the field can make more complicated research projects better.

Statisticians make sure that the research methods are sound and that the statistical analyses are done correctly, which adds to the study’s credibility.

In conclusion

Master’s papers are built around statistics. They take abstract ideas and turn them into real-world insights that help students make smart choices and make important contributions to the areas they choose. Using statistics is not only necessary, it’s also the key to making academic study more useful.

Mary Spears is a skilled and accomplished worker who is renowned for her hard work and knowledge in the areas of communications and marketing. With more than ten years of experience, Mary has constantly shown that she can create and carry out successful marketing plans that get results.

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Department of Statistics – Academic Commons Link to Recent Ph.D. Dissertations (2011 – present)

2022 Ph.D. Dissertations

Andrew Davison

Statistical Perspectives on Modern Network Embedding Methods

Sponsor: Tian Zheng

Nabarun Deb

Blessing of Dependence and Distribution-Freeness in Statistical Hypothesis Testing

Sponsor: Bodhisattva Sen / Co-Sponsor: Sumit Mukherjee

Elliot Gordon Rodriguez

Advances in Machine Learning for Compositional Data

Sponsor: John Cunningham

Charles Christopher Margossian

Modernizing Markov Chains Monte Carlo for Scientific and Bayesian Modeling

Sponsor: Andrew Gelman

Alejandra Quintos Lima

Dissertation TBA

Sponsor: Philip Protter

Bridgette Lynn Ratcliffe

Statistical approach to tagging stellar birth groups in the Milky Way

Sponsor: Bodhisattva Sen

Chengliang Tang

Latent Variable Models for Events on Social Networks

On Recovering the Best Rank-? Approximation from Few Entries

Sponsor: Ming Yuan

Sponsor: Sumit Mukherjee

2021 Ph.D. Dissertations

On the Construction of Minimax Optimal Nonparametric Tests with Kernel Embedding Methods

Sponsor: Liam Paninski

Advances in Statistical Machine Learning Methods for Neural Data Science

Milad Bakhshizadeh

Phase retrieval in the high-dimensional regime

Chi Wing Chu

Semiparametric Inference of Censored Data with Time-dependent Covariates

Miguel Angel Garrido Garcia

Characterization of the Fluctuations in a Symmetric Ensemble of Rank-Based Interacting Particles

Sponsor: Ioannis Karatzas

Rishabh Dudeja

High-dimensional Asymptotics for Phase Retrieval with Structured Sensing Matrices

Sponsor: Arian Maleki

Statistical Learning for Process Data

Sponsor: Jingchen Liu

Toward a scalable Bayesian workflow

2020 Ph.D. Dissertations

Jonathan Auerbach

Some Statistical Models for Prediction

Sponsor: Shaw-Hwa Lo

Adji Bousso Dieng

Deep Probabilistic Graphical Modeling

Sponsor: David Blei

Guanhua Fang

Latent Variable Models in Measurement: Theory and Application

Sponsor: Zhiliang Ying

Promit Ghosal

Time Evolution of the Kardar-Parisi-Zhang Equation

Sponsor: Ivan Corwin

Partition-based Model Representation Learning

Sihan Huang

Community Detection in Social Networks: Multilayer Networks and Pairwise Covariates

Peter JinHyung Lee

Spike Sorting for Large-scale Multi-electrode Array Recordings in Primate Retina

Statistical Analysis of Complex Data in Survival and Event History Analysis

Multiple Causal Inference with Bayesian Factor Models

New perspectives in cross-validation

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• Starting the research process

How to Choose a Dissertation Topic | 8 Steps to Follow

Published on November 11, 2022 by Shona McCombes and Tegan George. Revised on November 20, 2023.

Choosing your dissertation topic is the first step in making sure your research goes as smoothly as possible. When choosing a topic, it’s important to consider:

• Your institution and department’s requirements
• Your areas of knowledge and interest
• The scientific, social, or practical relevance
• The availability of data and resources
• The timeframe of your dissertation
• The relevance of your topic

You can follow these steps to begin narrowing down your ideas.

Table of contents

Step 1: check the requirements, step 2: choose a broad field of research, step 3: look for books and articles, step 4: find a niche, step 5: consider the type of research, step 6: determine the relevance, step 7: make sure it’s plausible, step 8: get your topic approved, other interesting articles, frequently asked questions about dissertation topics.

The very first step is to check your program’s requirements. This determines the scope of what it is possible for you to research.

• Is there a minimum and maximum word count?
• When is the deadline?
• Should the research have an academic or a professional orientation?
• Are there any methodological conditions? Do you have to conduct fieldwork, or use specific types of sources?

Some programs have stricter requirements than others. You might be given nothing more than a word count and a deadline, or you might have a restricted list of topics and approaches to choose from. If in doubt about what is expected of you, always ask your supervisor or department coordinator.

Start by thinking about your areas of interest within the subject you’re studying. Examples of broad ideas include:

• Twentieth-century literature
• Economic history
• Health policy

To get a more specific sense of the current state of research on your potential topic, skim through a few recent issues of the top journals in your field. Be sure to check out their most-cited articles in particular. For inspiration, you can also search Google Scholar , subject-specific databases , and your university library’s resources.

As you read, note down any specific ideas that interest you and make a shortlist of possible topics. If you’ve written other papers, such as a 3rd-year paper or a conference paper, consider how those topics can be broadened into a dissertation.

After doing some initial reading, it’s time to start narrowing down options for your potential topic. This can be a gradual process, and should get more and more specific as you go. For example, from the ideas above, you might narrow it down like this:

• Twentieth-century literature   Twentieth-century Irish literature   Post-war Irish poetry
• Economic history   European economic history   German labor union history
• Health policy   Reproductive health policy   Reproductive rights in South America

All of these topics are still broad enough that you’ll find a huge amount of books and articles about them. Try to find a specific niche where you can make your mark, such as: something not many people have researched yet, a question that’s still being debated, or a very current practical issue.

At this stage, make sure you have a few backup ideas — there’s still time to change your focus. If your topic doesn’t make it through the next few steps, you can try a different one. Later, you will narrow your focus down even more in your problem statement and research questions .

There are many different types of research , so at this stage, it’s a good idea to start thinking about what kind of approach you’ll take to your topic. Will you mainly focus on:

• Collecting original data (e.g., experimental or field research)?
• Analyzing existing data (e.g., national statistics, public records, or archives)?
• Interpreting cultural objects (e.g., novels, films, or paintings)?
• Comparing scholarly approaches (e.g., theories, methods, or interpretations)?

Many dissertations will combine more than one of these. Sometimes the type of research is obvious: if your topic is post-war Irish poetry, you will probably mainly be interpreting poems. But in other cases, there are several possible approaches. If your topic is reproductive rights in South America, you could analyze public policy documents and media coverage, or you could gather original data through interviews and surveys .

You don’t have to finalize your research design and methods yet, but the type of research will influence which aspects of the topic it’s possible to address, so it’s wise to consider this as you narrow down your ideas.

It’s important that your topic is interesting to you, but you’ll also have to make sure it’s academically, socially or practically relevant to your field.

• Academic relevance means that the research can fill a gap in knowledge or contribute to a scholarly debate in your field.
• Social relevance means that the research can advance our understanding of society and inform social change.
• Practical relevance means that the research can be applied to solve concrete problems or improve real-life processes.

The easiest way to make sure your research is relevant is to choose a topic that is clearly connected to current issues or debates, either in society at large or in your academic discipline. The relevance must be clearly stated when you define your research problem .

Before you make a final decision on your topic, consider again the length of your dissertation, the timeframe in which you have to complete it, and the practicalities of conducting the research.

Will you have enough time to read all the most important academic literature on this topic? If there’s too much information to tackle, consider narrowing your focus even more.

Will you be able to find enough sources or gather enough data to fulfil the requirements of the dissertation? If you think you might struggle to find information, consider broadening or shifting your focus.

Do you have to go to a specific location to gather data on the topic? Make sure that you have enough funding and practical access.

Last but not least, will the topic hold your interest for the length of the research process? To stay motivated, it’s important to choose something you’re enthusiastic about!

Most programmes will require you to submit a brief description of your topic, called a research prospectus or proposal .

Remember, if you discover that your topic is not as strong as you thought it was, it’s usually acceptable to change your mind and switch focus early in the dissertation process. Just make sure you have enough time to start on a new topic, and always check with your supervisor or department.

If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

Methodology

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

Formulating a main research question can be a difficult task. Overall, your question should contribute to solving the problem that you have defined in your problem statement .

However, it should also fulfill criteria in three main areas:

• Researchability
• Feasibility and specificity
• Relevance and originality

All research questions should be:

• Focused on a single problem or issue
• Researchable using primary and/or secondary sources
• Feasible to answer within the timeframe and practical constraints
• Specific enough to answer thoroughly
• Complex enough to develop the answer over the space of a paper or thesis
• Relevant to your field of study and/or society more broadly

You can assess information and arguments critically by asking certain questions about the source. You can use the CRAAP test , focusing on the currency , relevance , authority , accuracy , and purpose of a source of information.

Ask questions such as:

• Who is the author? Are they an expert?
• Why did the author publish it? What is their motivation?
• How do they make their argument? Is it backed up by evidence?

A dissertation prospectus or proposal describes what or who you plan to research for your dissertation. It delves into why, when, where, and how you will do your research, as well as helps you choose a type of research to pursue. You should also determine whether you plan to pursue qualitative or quantitative methods and what your research design will look like.

It should outline all of the decisions you have taken about your project, from your dissertation topic to your hypotheses and research objectives , ready to be approved by your supervisor or committee.

Note that some departments require a defense component, where you present your prospectus to your committee orally.

The best way to remember the difference between a research plan and a research proposal is that they have fundamentally different audiences. A research plan helps you, the researcher, organize your thoughts. On the other hand, a dissertation proposal or research proposal aims to convince others (e.g., a supervisor, a funding body, or a dissertation committee) that your research topic is relevant and worthy of being conducted.

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Thesis life: 7 ways to tackle statistics in your thesis.

By Pranav Kulkarni

Thesis is an integral part of your Masters’ study in Wageningen University and Research. It is the most exciting, independent and technical part of the study. More often than not, most departments in WU expect students to complete a short term independent project or a part of big on-going project for their thesis assignment.

Source : www.coursera.org

This assignment involves proposing a research question, tackling it with help of some observations or experiments, analyzing these observations or results and then stating them by drawing some conclusions.

Since it is an immitigable part of your thesis, you can neither run from statistics nor cry for help.

The penultimate part of this process involves analysis of results which is very crucial for coherence of your thesis assignment.This analysis usually involve use of statistical tools to help draw inferences. Most students who don’t pursue statistics in their curriculum are scared by this prospect. Since it is an immitigable part of your thesis, you can neither run from statistics nor cry for help. But in order to not get intimidated by statistics and its “greco-latin” language, there are a few ways in which you can make your journey through thesis life a pleasant experience.

Make statistics your friend

The best way to end your fear of statistics and all its paraphernalia is to befriend it. Try to learn all that you can about the techniques that you will be using, why they were invented, how they were invented and who did this deed. Personifying the story of statistical techniques makes them digestible and easy to use. Each new method in statistics comes with a unique story and loads of nerdy anecdotes.

If you cannot make friends with statistics, at least make a truce

If you cannot still bring yourself about to be interested in the life and times of statistics, the best way to not hate statistics is to make an agreement with yourself. You must realise that although important, this is only part of your thesis. The better part of your thesis is something you trained for and learned. So, don’t bother to fuss about statistics and make you all nervous. Do your job, enjoy thesis to the fullest and complete the statistical section as soon as possible. At the end, you would have forgotten all about your worries and fears of statistics.

Visualize your data

The best way to understand the results and observations from your study/ experiments, is to visualize your data. See different trends, patterns, or lack thereof to understand what you are supposed to do. Moreover, graphics and illustrations can be used directly in your report. These techniques will also help you decide on which statistical analyses you must perform to answer your research question. Blind decisions about statistics can often influence your study and make it very confusing or worse, make it completely wrong!

Simplify with flowcharts and planning

Similar to graphical visualizations, making flowcharts and planning various steps of your study can prove beneficial to make statistical decisions. Human brain can analyse pictorial information faster than literal information. So, it is always easier to understand your exact goal when you can make decisions based on flowchart or any logical flow-plans.

Source: www.imindq.com

Find examples on internet

Although statistics is a giant maze of complicated terminologies, the internet holds the key to this particular maze. You can find tons of examples on the web. These may be similar to what you intend to do or be different applications of the similar tools that you wish to engage. Especially, in case of Statistical programming languages like R, SAS, Python, PERL, VBA, etc. there is a vast database of example codes, clarifications and direct training examples available on the internet. Various forums are also available for specialized statistical methodologies where different experts and students discuss the issues regarding their own projects.

Comparative studies

Much unlike blindly searching the internet for examples and taking word of advice from online faceless people, you can systematically learn which quantitative tests to perform by rigorously studying literature of relevant research. Since you came up with a certain problem to tackle in your field of study, chances are, someone else also came up with this issue or something quite similar. You can find solutions to many such problems by scouring the internet for research papers which address the issue. Nevertheless, you should be cautious. It is easy to get lost and disheartened when you find many heavy statistical studies with lots of maths and derivations with huge cryptic symbolical text.

When all else fails, talk to an expert

All the steps above are meant to help you independently tackle whatever hurdles you encounter over the course of your thesis. But, when you cannot tackle them yourself it is always prudent and most efficient to ask for help. Talking to students from your thesis ring who have done something similar is one way of help. Another is to make an appointment with your supervisor and take specific questions to him/ her. If that is not possible, you can contact some other teaching staff or researchers from your research group. Try not to waste their as well as you time by making a list of specific problems that you will like to discuss. I think most are happy to help in any way possible.

Talking to students from your thesis ring who have done something similar is one way of help.

Sometimes, with the help of your supervisor, you can make an appointment with someone from the “Biometris” which is the WU’s statistics department. These people are the real deal; chances are, these people can solve all your problems without any difficulty. Always remember, you are in the process of learning, nobody expects you to be an expert in everything. Ask for help when there seems to be no hope.

Apart from these seven ways to make your statistical journey pleasant, you should always engage in reading, watching, listening to stuff relevant to your thesis topic and talking about it to those who are interested. Most questions have solutions in the ether realm of communication. So, best of luck and break a leg!!!

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There are 4 comments.

A perfect approach in a very crisp and clear manner! The sequence suggested is absolutely perfect and will help the students very much. I particularly liked the idea of visualisation!

You are write! I get totally stuck with learning and understanding statistics for my Dissertation!

Statistics is a technical subject that requires extra effort. With the highlighted tips you already highlighted i expect it will offer the much needed help with statistics analysis in my course.

this is so much relevant to me! Don’t forget one more point: try to enrol specific online statistics course (in my case, I’m too late to join any statistic course). The hardest part for me actually to choose what type of statistical test to choose among many options

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Home > Statistics > Dissertations, Theses, and Student Work

Statistics, Department of

Department of statistics: dissertations, theses, and student work.

Examining the Effect of Word Embeddings and Preprocessing Methods on Fake News Detection , Jessica Hauschild

Exploring Experimental Design and Multivariate Analysis Techniques for Evaluating Community Structure of Bacteria in Microbiome Data , Kelsey Karnik

Human Perception of Exponentially Increasing Data Displayed on a Log Scale Evaluated Through Experimental Graphics Tasks , Emily Robinson

Factors Influencing Student Outcomes in a Large, Online Simulation-Based Introductory Statistics Course , Ella M. Burnham

Comparing Machine Learning Techniques with State-of-the-Art Parametric Prediction Models for Predicting Soybean Traits , Susweta Ray

Using Stability to Select a Shrinkage Method , Dean Dustin

Statistical Methodology to Establish a Benchmark for Evaluating Antimicrobial Resistance Genes through Real Time PCR assay , Enakshy Dutta

Group Testing Identification: Objective Functions, Implementation, and Multiplex Assays , Brianna D. Hitt

Community Impact on the Home Advantage within NCAA Men's Basketball , Erin O'Donnell

Optimal Design for a Causal Structure , Zaher Kmail

Role of Misclassification Estimates in Estimating Disease Prevalence and a Non-Linear Approach to Study Synchrony Using Heart Rate Variability in Chickens , Dola Pathak

A Characterization of a Value Added Model and a New Multi-Stage Model For Estimating Teacher Effects Within Small School Systems , Julie M. Garai

Methods to Account for Breed Composition in a Bayesian GWAS Method which Utilizes Haplotype Clusters , Danielle F. Wilson-Wells

Beta-Binomial Kriging: A New Approach to Modeling Spatially Correlated Proportions , Aimee Schwab

Simulations of a New Response-Adaptive Biased Coin Design , Aleksandra Stein

MODELING THE DYNAMIC PROCESSES OF CHALLENGE AND RECOVERY (STRESS AND STRAIN) OVER TIME , Fan Yang

A New Approach to Modeling Multivariate Time Series on Multiple Temporal Scales , Tucker Zeleny

A Reduced Bias Method of Estimating Variance Components in Generalized Linear Mixed Models , Elizabeth A. Claassen

NEW STATISTICAL METHODS FOR ANALYSIS OF HISTORICAL DATA FROM WILDLIFE POPULATIONS , Trevor Hefley

Informative Retesting for Hierarchical Group Testing , Michael S. Black

A Test for Detecting Changes in Closed Networks Based on the Number of Communications Between Nodes , Christopher S. Wichman

GROUP TESTING REGRESSION MODELS , Boan Zhang

A Comparison of Spatial Prediction Techniques Using Both Hard and Soft Data , Megan L. Liedtke Tesar

STUDYING THE HANDLING OF HEAT STRESSED CATTLE USING THE ADDITIVE BI-LOGISTIC MODEL TO FIT BODY TEMPERATURE , Fan Yang

Estimating Teacher Effects Using Value-Added Models , Jennifer L. Green

SEQUENCE COMPARISON AND STOCHASTIC MODEL BASED ON MULTI-ORDER MARKOV MODELS , Xiang Fang

DETECTING DIFFERENTIALLY EXPRESSED GENES WHILE CONTROLLING THE FALSE DISCOVERY RATE FOR MICROARRAY DATA , SHUO JIAO

Spatial Clustering Using the Likelihood Function , April Kerby

FULLY EXPONENTIAL LAPLACE APPROXIMATION EM ALGORITHM FOR NONLINEAR MIXED EFFECTS MODELS , Meijian Zhou

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Master Thesis

Possible Topics:

• The evolution of ethnic wage inequality in Germany ( Hase )

• Do unions reduce the ethnic wage gap? ( Hase )

• Does the minimum wage reduce the ethnic wage gap? ( Hase )

• The trade-off effect of family-friendly policy on women’s wage ( Liang )

• The homeownership gap between immigrants and natives and heterogeneous impacts of homeownership on life satisfaction (Liang)

• COVID-19, working from home and wage inequality (Liang)

• Do household income shocks lead to divorces and unstable families? (Moog)

• The effect of increased gas prices on working hours (Moog/Schank )

• The effect of having internet at home on the probability to move to another location ( Schank )

• The effect of having internet at home on people’s social behavior ( Schank )

• The effect of the public smoking ban in Germany on people’s propensity to go out ( Schank )

• Is the public smoking ban in Germany good or bad for pubs and restaurants? ( Schank )

• The effect of public holidays on worker productivity ( Schank )

• The effect of team diversity (in respect of e.g. age, nationality, experience) on team performance in the German soccer/ volleyball league ( Voigt )

• Value inheritance: The effect of parents' academic values on children's ambitions ( Voigt )

• Does the presence of children reduce the amount of training on the job and what is the associated wage penalty? ( Carow )

• Determinants of the duration of parental leaves of fathers ( Carow )

For further information, you can contact the person mentioned in brackets. You can also contact us with your own suggestion.

Thesis currently in process:

• Employment responses to changing gas prices (Jan Lucas Wilhelm)

Completed dissertations:

• Evaluating potentials of synthetic dataset provision for research and statistical offices in Germany (Yannik Garcia Ritz)

• Trends in immigrant-native wage inequality in Germany (Thorsten Aron)

• Der Einfluss des gesetzlichen Mindestlohnes in Deutschland auf Stundenlöhne und Monatseinkommen (Lars Chittka)

• Does the minimum wage reduce the ethnic wage gap? (Hira Kücük)

• Internet access and school performance: evidence from the German SOEP (Joao Felipe Mayer Saucedo)

• The effect of gender diverse supervisory boards on the gender remuneration gap at executive boards: An empirical analysis for Germany (Benedikt Brand)

• Determinants of paid and unpaid overtime: an international comparison of Germany and the UK (Julia Hörsch)

• Determinants and dynamics in multiple job holding - evidence from the German Socio-Economic Panel (Alexander Moog)

• The effect of low-emission zones on air quality in German cities (Sebastian Gradel)

• The impact of German minimum wage policy on workers subjective well-being (Maria del Pilar Triana Torres)

• The impact of German minimum wage policy on the gender wage gap (Laura Fleckenstein)

• The effect of working hours mismatch on job satisfaction: evidence for workers with children (Daniela Maier)

• Determinants of success in sports -the influence of visitors on the results of professional soccer matches (Christian Orthey)

• Out of sight out of mind - the effects of former loan agreements on future transfer fees within European Football (Tiago Pereira)

• The effect of team diversity on team performance in the German soccer league (Vasil Yordanov)

• The effect of the Volkswagen emission scandal on the sales of different automobile brands (Jonas Jähnke)

• The effect of women on supervisory boards on the employees' gender wage gap. Evidence from German linked employee-plant-firm data (Johannes Carow)

• Determinants of flight irregularities: an empirical analysis for Lufthansa Technik (Tobias Hausmann)

• Using Monte Carlo simulations to compare OLS and Matching estimators (Maximilian Lüke)

• The development of wage inequality in Germany from 2006 to 2016 - comparison of results based on the GSOEP and the GSES (Rebekka Schnitzler)

• The effect of gender diverse supervisory boards on top executive's compensation in Germany: An empirical analysis (Laura Bilavski)

• Labour market returns to physical exercise in Germany. An empirical analysis (Matthias Dincher)

• The effects of regional allocation of refugees on local voting outcomes - empirical evidence from the 2016 regional elections in Hesse (Germany) (Mathias Lück)

• Do women participate less in further education? (Linh Hoang)

• Determinants of internal and external job promotion - an empirical analysis with German SOEP data (Nicole Nelling)

• The effect of parental age at birth on educational outcomes and wages: an empirical analysis with the German SOEP (Marc Diederichs)

• The relationship of board gender diversity and stock price informativeness: an empirical analysis of the DAX 160 companies (Stephan Eck)

• Does the German statutory minimum wage affect working hours? An empirical investigation (Christian Düben)

• Are employees with fixed-term contracts less absent from work than employees with permanent contracts? An empirical analysis using the German Socio-Economic Panel (Hannah Schwabl)

• The role of aid to the health sector in attracting FDI: empirical evidence from Africa (Franziska Ulrich)

• Using simulations to evaluate different econometric methods to estimate dynamic non-linear models (Alexander Basan)

• Gender diversity, critical mass and firm performance: new evidence from German boardrooms (Vera Steitz)

• Job search behavior of unemployment-benefit-II recipients. An empirical analysis using PASS (Lenin Castillo)

• Has internet increased the job finding rate? An empirical analysis (Manuel Denzer)

• Using simulations to evaluate different methods to estimate binary response models with a binary endogenous explanatory variable (Annelen Carow)

• Do wages rise more in large firms? Evidence for Germany (Ying Liang)

• The effect of smoking behavior on labor market and health outcomes (Yingjie Huang)

• Strategic alliances among venture backed companies - empirical evidence from biotechs (Leonhard Brinster)

• Persistence in welfare-receipt. An empirical analysis using the panel study "Labour Market and Social Security" (PASS) (Stefan Schwarz)

• What are the determinants of rent prices in Germany? An empirical analysis (Sarim Khalid)

• Job mobility and risk aversion. An empirical analysis using the German Socio-Economic Panel (Sandra Achten)

• The impact of natural resources on economic growth using simulated maximum likelihood methods to estimate country-specific coefficients (Giacomo Benini)

• Institutional change, openness and development: evidence from Africa (Felix Giorgio Amato)

• Trade liberalization and price pass-through: evidence from the world coffee market (Victor Gimenez Perales)

• Analysis of the impact of health facility condition on educational outcomes of elementary school students: evidence from Uganda (Jan-Stephen Welsch)

• An analysis of forecasting methods with the example of the German GDP forecasting (Christian Endres)

• Does winning today increase the chances of winning tomorrow? An empirical analysis of football data (Julius Nick)

• Determinanten der CDS-Spreads - eine dynamische Paneldatenanalyse - (Jörg Geier)

• Women labor force participation and economic development: evidence from developing countries (Farhan Azmat)

• Die Determinanten nationaler Migration (Samir Ben Naceur, Diplom)

• Human capital and its impact - income differentials between Bachelor, Master and Diploma graduates (Nora Nickig)

• Children and their parents labor supply: evidence from Germany (Eni Bilbili)

• The determinants of China's urban house price: evidence from provincial panel data in mainland China (Fan Yang)

• The construction of a regional price index for the German federal state of Hesse (Stefanie Käuser und Mathias Bieg)

• To move or not to move: the effects of wage, unemployment and house price differentials on the interregional migration decision in Germany (Lorna Syme)

• Wage and employment effects of immigration to Russia (Evgenia Poliakova)

• Theory and empirical applications of the European airline market (Chunxiao Ma)

• An analysis of the economic transition and income inequality in China (Xiaoli Jiang)

• Horizontale Unternehmenszusammenschlüsse: Motive und Wohlfahrtseffekte (Atahar Ahmad, Diplom)

• Auswirkungen von aktivierender Arbeitsmarktpolitik im Rahmen von Such- und Matchingmodellen (Patrick Könsgen, Diplom)

• Labour market dynamics of couples receiving welfare. An empirical analysis using PASS (Lisa Leschnig)

• Die Lohnkurve: eine empirische Schätzung mit Daten der Verdienststrukturerhebung 2006 (Thorsten Ritter, Diplom)

• Studentische Preisdiskriminierung am Mainzer Staatstheater (Sarah Anna Mediouni, Diplom)

• Eine Analyse der Reaktion des deutschen Arbeitsmarktes auf die Finanzkrise (Daniel Vorreiter, Diplom)

• Preisdiskriminierung im Schienenpersonenfernverkehr: Eine ökonomische Analyse in Theorie und Praxis – unter besonderer Berücksichtigung des InterConnex“ (Vera Plachetka, Diplom)

Supervisors and topics for master's theses in statistics

As part of his or her master's study, a student should write a thesis. There are two options for the thesis: a long thesis corresponding to one year full time work, and a short thesis corresponding to one semester's full time work. The work on a long thesis typically starts in the second semester of the master's study (as described here ), while the work on a short thesis should be done during the last semester of the master's study. Below we give an overview of possible supervisors and topic for the master's thesis. 

Riccardo De Bin

My main field of research is statistical learning ( STK-IN4300 ), with focus on methodological issues related to high-dimensional data. In particular, I am strongly interested in the statistical boosting, a method which combines the powerfulness of a machine-learning approach and the interpretability of a statistical model. In the same context of computational approaches, I am also interested in resampling-based methods for variable selection, data analysis and model averaging. In addition, I have also more theoretical interests, mainly in the field of asymptotic theory, where I am focusing on methods for the treatment of nuisance parameters.

Examples of master's theses that I have supervised:

Vegard Stikbakke. A boosting algorithm to extend first-hitting-time models to a high-dimensional survival setting , Long thesis, 2019.

Jonas Gjesvik. Statistical modelling of Goalkeepers in the Norwegian Tippeliga ,Long thesis, 2019.

Ingrid Kristine Glad

Over several years, my main research interest has been in developing methodology tailored for the analysis of high dimensional data, with links to topics in f.ex.  STK-IN4300 .

I am heavily involved in the research for innovation center for big and complex data problems,  BigInsight , as researcher and co-director. BigInsight would like to offer master projects within most BigInsight topics. For me it is most actual to supervise master projects related to high dimensional, high frequency sensor data, mainly from the maritime sector, see the BigInsight web pages (Innovation Objective Sensor Systems). 

I have also been working for several years with high dimensional genomic data connected to cancer research. I can offer master projects related to statistical analysis of genomic and/or epigenetic data, where the high dimensionality of the data (especially p>n) leads to interesting methodological challenges.

Martin Tveten:  Multi-Stream Sequential Change Detection Using Sparsity and Dimension Reduction , long thesis, 2017

Camilla Lingjærde: Tailored Graphical Lasso for Data Integration in Gene Network Reconstruction , long thesis, 2019

Ingrid Hobæk Haff

My main field of research over the past years has been multivariate modelling, in particular copulas, with applications within for instance finance, insurance and climate. I am also involved in BigInsight , as a researcher and co-director, and also supervise master’s theses with topics from this centre. More specifically I work on problems related to personalised fraud detection, i.e. constructing systems for uncovering tax fraud, insurance fraud and money laundering, which involves high-dimensional, imbalanced data. Further, I am engaged in the new convergence environment ImmunoLingo , a transdisciplinarily project, whose aim is to decipher the molecular language of adaptive immunity. I will also propose master thesis topics from this project.

Daniel Piacek: Detecting fraud using information from social networks . Long thesis, 2017

Eirik Lødøen Halsteinlid: Addressing collinearity and class imbalance in logistic regression for statistical fraud detection . Long thesis, 2019.

Nils Lid Hjort

I work in several areas of theoretical and applied statistics, with some key words being model building, model selection and model averaging, confidence distributions, estimation theory, survival analysis, Bayesian nonparametrics, stability and change. I led the research project group FocuStat with several PostDocs, PhDs, and Master level students , from 2014 to 2018, and several of our themes are continued, in partly new directions. Two projects, flowing from FocuStat themes, are From Processes to Models (ways of constructing better models for data) and Stability and Change (theory for finding changes, and conditions for stability, with application to war-and-peace data).

You may check the FocuStat webpage, including blog posts, with various themes that may also lead to Master thesis projects.

The majority of my students are working on the theoretical side of the spectrum, but from time to time I also supervise more applied projects (examples being recommender systems for finn.no; analysis of track and field data; examination of the forensic information used to convict Fredrik Fasting Torgersen for murder in 1958; the keeper's role in football matches; Markov chains for modelling escalation in armed conflicts).

If interested, check the list of Master- and PhD-students at the FocuStat website , which includes brief descriptions of and links to their projects and theses.

Sven Ove Samuelsen

My field is event history analysis (cf. STK4080 ) and in particular I have been interested in theoretical developments and applications in epidemiology. Some of the master’s theses I have supervised have had a focus on developments of case-control studies and similar epidemiological designs with a time to event perspective. Others master’s theses have been more directly connected to analyses of specific epidemiological data sets. The problems and data sets for the master’s theses often turn up in connection with collaborations with researchers at the Norwegian Institute of Public Health where I work part time. I am also involved in the strategic research initiative Pharmatox   at the University of Oslo where we will study possible effects of medicines taken during pregnancy on neurodevelopment in childhood.  

Morten Madshus:  A Match Too Much? - A simulation study on overmatching in nested case-control studies.  Long thesis 2019

Lena Johansen: Metoder og metodiske utfordringer for matchede kohortstudier. Long thesis 2018

Simon Lergenmuller: Two-stage predictor substitution for time-to-event data . Long thesis, 2017.

My research themes are often connected to Bayesian modelling and analysis, for example some type of space-time modelling or model diagnostics. I am a participant in the Research-based Innovation (SFI) BigInsight . Projects that are motivated by applications include one where we model the viral spread of products on social networks, a project which is in collaboration with Telenor. Another concerns a new Bayesian recommender system for clicking data. ‘Clicking data’, the history that consumers have of clicking on webpages, reveal their preferences. Such data arise in very many areas in the digital world, including business (e.g. a company selling products online) and entertainment (e.g. Spotify, Netflix, NRK). A recommender system aims at personalised recommendations based on the history of the consumer and other consumers. For this project we collaborate both with NRK and finn.no. More theoretically motivated is my interest in model diagnostics, mainly concerning checking for possible modelling conflicts at the node-level of (Bayesian) hierarchical models. A possible master project could be connected to this field.

Examples of master’s theses that I have supervised:

Jonas Fredrik Schenkel:  Collaborative Filtering for Implicit Feedba ck: Investigating how to improve NRK TV's recommender system by including context  . Long thesis, 2017.

Jenine Gaspar Corrales: Analyzing and Predicting Demographics of NRK's Digital Users . Long thesis, 2019.

Geir Storvik

My main fields of research are (Bayesian) computational statistics and Monte Carlo methods. In particular, analysis of data that have a dependence structure in time and/or space is central in many of my projects. Such problems impose challenges both at the modelling stage and with respect to computation. I am involved in  CELS , a multidisciplinary center for computational inference in evolutionary life science at the University of Oslo. Problems considered are within ecology, evolution but also forensic science. Analysis of big data is also possible through my engagement in  BigInsight , a new center for Research-based Innovation (SFI), where huge amounts of multivariate sensor data needs to be analysed. I also have a part time position at  Norwegian Computing Center (Norsk Regnesentral)  where I currently am involved in projects concerning marine resources (estimation of abundance etc). 

Possible master-project

• Useful background:  STK4021 ,  STK4051

Martin Gjesdal Bjørndal: Distance Metrics in Variant Graphs , Long thesis, 2017

Kjersti Moss:  The Poisson-Binomial Model for Fish Abundance Estimation: With Applications to Northeast Arctic cod . Long thesis, 2015

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Hire me as a consultant to work on the data analysis (statistical analysis) portion of your dissertation or thesis.

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Saint Louis University’s Department of Mathematics and Statistics offers undergraduate and graduate students a wide variety of courses on a diverse range of topics.

Be sure to check out the College of Arts and Sciences Academic Catalog for official course listings.

Undergraduate Courses

MATH 0225: Basic Mathematics Prep course designed to expose students to signed Numbers: common fractions, decimals and percentages; ratio and proportion; area and volume; powers and roots; algebraic expressions and operations; linear equations; basic trigonometric functions; factoring polynomials. Three credit hours.

MATH 0235: Introduction Elementary Algebra Three credit hours. Mathematics (Ps) Department

MATH 0240: Introduction to Elementary Algebra I MATH 0240 and MATH 0250 together cover the same material as MATH 0260, but in two semesters. Credit not given for both MATH 0240 and MATH 0260. Fall semester. Two credit hours.

MATH 0250: Elementary Algebra II MATH 0240 and MATH 0250 together cover the same material as MATH 0260, but in two semesters. Credit not given for both MATH 0250 and MATH 0260. Fall and spring semesters. Prerequisite: Grade of “C−” or better in Math 0240. Two credit hours.

MATH 0260: Intermediate Algebra Radicals, exponents, first degree equations, simultaneous equations, quadratic equations, functions, graphs, logarithms, polynomials. Credit not given for both MATH 0260 and any of the following: MATH 0240, MATH 0250. Fall and spring semesters. Prerequisite: Math Index at least 700. Three credit hours.

MATH 1200: College Algebra Polynomials; rational functions; exponential and logarithmic functions; conic sections; systems of equations; and inequalities. Intended for students needing more preparation before taking MATH 1320: Survey of Calculus, MATH 1400: Pre-calculus. Fall, spring, and summer. Prerequisite: Math Index at least 800, or a grade of “C−” or better in MATH 0260: Intermediate Algebra. Three credit hours.

MATH 1220: Finite Mathematics Linear equations and straight lines, matrices, sets and counting, probability and statistics, the mathematics of finance, and logic. Fall and spring semesters. Prerequisite: Math-Index at least 750 or grade of “C−” or better in MATH 0260: Intermediate Algebra. Three credit hours.

MATH 1240:Mathematics and the Art of M.C. Escher An inquiry course open to all undergraduates. In this course we will discover how M.C. Escher created some of his artwork. The art of M.C. Escher will be used to explore such topics as: polygons, transformations, tessellations, and wallpaper patterns. Taught in a computer classroom. Prerequisite: Math-Index at least 750 or grade of “C−” or better in MATH 1200: College Algebra or equivalent. (An understanding beyond MATH 0260 is needed.) Thee credit hours.

MATH 1240: Mathematics and the Art of M.C. Escher A SLU Inquiry Seminar. The art of M.C. Escher is used to explore topics in geometry such as symmetry, tessellations, wallpaper patterns, the geometry of the sphere and hyperbolic geometry. Taught in a computer classroom. Fall and spring. Prerequisites: 3.5 years of high school mathematics or a grade of C- or better in MATH 1200. Three credit hours.

MATH 1250: Mathematical Thinking in Real World An inquiry course open to all undergraduates. In this course, aimed at students in the humanities and social sciences, we study some of the greatest ideas of mathematics that are often hidden from view in lower division courses. Topics selected from number theory, the infinite, geometry, topology, chaos and fractals, and probability. Taught in a computer classroom. Prerequisite: Math-Index at least 750 or a grade of “C−” or better in MATH 1200: College Algebra or equivalent. (An understanding beyond MATH 0260 is needed.) Three credit hours.

MATH/STAT 1260: Statistics Including Sports and Politics An inquiry course open to all undergraduates. Producing data through the use of samples and experiments; organizing data through graphs and numbers that describe the distribution of the data of one variable or the relationship between two variables; probability; statistical inference including confidence intervals and tests of significance. Prerequisite: Math Index at least 750 or a grade of “C−” or better in MATH 1200. Three credit hours.

MATH/STAT 1300: Elementary Statistics with Computers Data production and analysis; probability basics, distributions; sampling, estimation with confidence intervals, hypothesis testing, t-test; correlation and regression; crosstabulations and chi-square. Students learn to use a statistical package such as SPSS. Prerequisite: Math Index at least 900 or a grade of "C−” or better in MATH 1200: College Algebra or equivalent. Three credit hours.

MATH 1320: Survey of Calculus Introductory differential and integral calculus, optimization and rate problems, calculus of rational, exponential and logarithmic functions, partial derivatives and applications. Fall, spring and summer. Math Index at least 900 or a grade of “C−” or better in MATH 1200: College Algebra. Three credit hours.

MATH 1400: Pre-calculus Trigonometric functions, graphing, identities, solving triangles, inverse trigonometric functions, polar coordinates, complex numbers, and analytic geometry. Fall and spring semesters. Prerequisite: Math Index at least 950 or a grade of “C−” or better in MATH 1200: College Algebra. Three credit hours.

MATH 1510: Calculus I Elementary functions; differentiation and integration from geometric and symbolic viewpoints; limits, continuity; applications. Fall and spring semesters. Prerequisite: Math Index at least 1020 or a grade of “C−” or better in MATH 1400: Pre-calculus. Four credit hours. 1818 Advanced College Credit

MATH 1520: Calculus II Symbolic and numerical techniques of integration, indeterminate forms, infinite series, power series, Taylor series, differential equations; polar coordinates, applications. Prerequisite: Score at least 4 on the Calculus AP Test (AB), Math-Index at least 1050, or a grade of “C−” or better in MATH 1510: Calculus I. 4 Credit Hours. 1818 Advanced College Credit

MATH 1650: Cryptology An inquiry course open to all undergraduates. Aimed at students who require a course at the level of calculus or higher and who are interested in the mathematical basis for cryptology systems. Topics include permutation based codes, block cipher schemes and public key encryption. Prerequisite: Four years of high school mathematics. Three credit hours.

MATH 1660: Discrete Mathematics Concepts of discrete mathematics used in computer science; sets, sequences, strings, symbolic logic, proofs, mathematical induction, sums and products, number systems, algorithms, complexity, graph theory, finite state machines. Prerequisite: A grade of “C−” or better in MATH 1200: College Algebra or equivalent. Three credit hours.

MATH 1990: Honors Course in Mathematics Offered occasionally. One to three credit hours.

MATH 2150: Computational Linear Algebra Vectors, matrices and matrix operations, determinants, systems of linear equations, Gaussian elimination, direct factorization, finite-precision arithmetic and round-off, condition number, iterative methods, vector and matrix norms, eigenvalues and eigenvectors, CAS package. Three credit hours.

MATH 2530: Calculus III Three-dimensional analytic geometry, vector-valued functions, partial differentiation, multiple integration, and line integrals. Fall and spring semesters. Prerequisite: A grade of “C−” or better in MATH 2530: Calculus III. Four credit hours.

MATH 2660: Principles of Mathematics Introduction to the basic techniques of writing proofs and to fundamental ideas used throughout mathematics. Topics covered include formal logic, proof by contradiction, set theory, mathematical induction and recursion, relations and congruence, functions. Fall and spring semesters. Prerequisite: A grade of “C−” or better in MATH 1510: Calculus I. Three credit hours.

MATH 2690: Mathematical Problem Solving Intended primarily to train students for the William Lowell Putnam Mathematical Competition, this course covers a mélange of ingenious techniques for solving mathematics problems cutting across the entire undergraduate spectrum, including precalculus, calculus, combinatorics, probability, inequalities. Coverage tailored to students’ interests. May be repeated for credit. Fall semester. Prerequisite: None. One credit hour.

MATH 2930: Special Topics One to four credit hours.

MATH 2980: Independent Study Prior approval of sponsoring professor and chair required. Zero to three credit hours. Independent study

MATH 2990: Honors Course in Mathematics One to three credit hours.

MATH 3110: Linear Algebra for Engineers Systems of linear equations, matrices, linear programming, determinants, vector spaces, inner product spaces, eigenvalues and eigenvectors, linear transformations, and numerical methods. Credit not given for both MATH 3110 and MATH 3120. Spring semester. Prerequisite: A grade of “C−” or better in MATH 1520: Calculus II and a knowledge of vectors. Three credit hours.

MATH 3120: Introduction to Linear Algebra Matrices, row operations with matrices, determinants, systems of linear equations, vector spaces, linear transformations, inner products, eigenvalues and eigenvectors. Credit not given for both MATH 3120 and MATH 3110. Fall and spring semesters. Prerequisite: MATH 2530: Calculus III and MATH 2660: Principles of Math. Three credit hours.

MATH 3230: Vector Analysis Vector algebra, differential and integral calculus of vector functions, linear vector functions and dyadics, applications to geometry, particle and fluid mechanics, theory of vector fields. Offered occasionally. Prerequisite: MATH 2530: Calculus III. Three credit hours.

MATH 3240: Numerical Analysis Review of calculus; root finding, nonlinear systems, interpolation and approximation; numerical differentiation and integration. Alternate spring semesters. Prerequisite: MATH 2530: Calculus III. Three credit hours.

MATH 3270: Advanced Mathematics for Engineers Vector algebra; matrix algebra; systems of linear equations; eigenvalues and eigenvectors; systems of differential equations; vector differential calculus; divergence, gradient and curl; vector integral calculus; integral theorems; Fourier series with applications to partial differential equations. Fall and spring semesters. Prerequisite: MATH 3550: Differential Equations. Three credit hours.

MATH 3550: Differential Equations Solution of ordinary differential equations, higher order linear equations, constant coefficient equations, systems of first order equations, linear systems, equilibrium of nonlinear systems, Laplace transformations. Prerequisite: MATH 2530: Calculus III. Three credit hours.

MATH 3600: Combinatorics Advanced counting methods: permutations and combinations, generalized permutations and combinations, recurrance relations, generating functions; algorithms: graphs and digraphs, graph algorithms: minimum-cost spanning trees, shortest path, network flows; depth first and breadth-first searches; combinatorial algorithms: resource scheduling, bin-packing: algorithmic analysis and NP completeness. Three credit hours.

MATH 3760: Financial Mathematics Theory of interest material for the Financial Mathematics exam of the Society of Actuaries. Time permitting, supplemental material covering financial derivatives will be discussed. Prerequisite: MATH 2530: Calculus III. Three credit hours.

MATH 3800: Elementary Theory of Probability Counting theory; axiomatic probability, random variables, expectation, limit theorems. Applications of the theory of probability to a variety of practical problems. Credit not given for both MATH 3800 and either MATH 3810 or MATH 4800. Fall semester. Prerequisite: MATH 2530: Calculus III. Three credit hours.

MATH 3810: Probability and Statistics for Engineers Analyzing and producing data; probability; random variables; probability distributions; expectation; sampling distributions; confidence intervals; hypothesis testing; experimental design; regression and correlation analysis. Credit not given for both MATH 4880 and either MATH 4810 or MATH 4820. Fall and spring semesters. Prerequisite: MATH 2530: Calculus III. Three credit hours.

MATH 3850: Foundations of Statistical Analysis Descriptive statistics, probability distributions, random variables, expectation, independence, hypothesis testing, confidence intervals, regression and ANOVA. Applications and theory. Taught using statistical software. Credit not given for both MATH/STAT 3810 and MATH/STAT 3850. Fall and Spring semesters. Prerequisite: MATH 2530: Calculus III. Three credit hours.

MATH 4050: History of Mathematics The development of several important branches of mathematics, including numeration and computation, algebra, non-Euclidean geometry, and calculus. Offered every other spring (even years). Prerequisite: MATH 1520: Calculus II. Three credit hours.

MATH 4110: Introduction to Abstract Algebra Elementary properties of the integers, sets and mappings, groups, rings, integral domains, division rings and fields. Fall semester. Prerequisite: MATH 3120: Intro to Linear Algebra. Three credit hours.

MATH 4120: Linear Algebra Advanced linear algebra, including linear transformations and duality, elementary canonical forms, rational and Jordan forms, inner product spaces, unitary operators, normal operators and spectral theory. Alternate spring semesters. Prerequisite: MATH 4110. Three credit hours.

MATH 4150: Number Theory Introduction to algebraic number theory. Topics will include primes, Chinese remainder theorem, Diophantine equations, algebraic numbers and quadratic residues. Additional topics will vary from year to year. Alternate spring semesters. Prerequisite: MATH 4110. Three credit hours.

MATH 4210: Introduction to Analysis Real number system, functions, sequences, limits, continuity, differentiation, integration and series. Fall semester. Prerequisite: MATH 2530 and MATH 3120. Three credit hours.

MATH 4220: Metric Spaces Set theory, metric spaces, completeness, compactness, connected sets, category. Spring semester. Prerequisite: MATH 4210. Three credit hours.

MATH 4230: Multivariable Analysis Introduction to analysis in multidimensional Euclidean space. Sequences and Series of functions, Differentiability, Integrability, Inverse and Implicit function theorems, Fundamental Theorems of Multivariable Calculus (Green's Theorem, Stokes Theorem, Divergence Theorem). Spring semester. Prerequisite: MATH 4210. Three credit hours.

MATH 4310: Introduction to Complex Variables Complex number system and its operations, limits and sequences, continuous functions and their properties, derivatives, conformal representation, curvilinear and complex integration, Cauchy integral theorems, power series and singularities. Fall semester. Prerequisite: MATH 2530: Calculus III. Three credit hours.

MATH 4320: Complex Variables II This course is a continuation of MATH 4310. Topics covered include series, residues and poles, conformal mapping, integral formulas, analytic continuation, and Riemann surfaces. Spring semester. Prerequisite: MATH 4310. Three credit hours.

MATH 4360: Geometric Topology An introduction to the geometry and topology of surfaces and three dimensional spaces. Topics covered Include Euclidean, spherical and hyperbolic geometry, topology of surfaces, knot theory, and the fundamental group. Prerequisite: MATH 4310. Three credit hours.

MATH 4410: Foundations of Geometry Historical background of the study of Euclidean geometry; development of two-dimensional Euclidean geometry from a selected set of postulates. Offered occasionally. Prerequisite: MATH 2530: Calculus III. Three credit hours.

MATH 4430: Non-Euclidean Geometry The rise and development of the non-Euclidean geometries with intensive study of plane hyperbolic geometry. Offered occasionally. Prerequisite: MATH 1510: Calculus I. Three credit hours.

MATH 4480: Differential Geometry Classical theory of smooth curves and surfaces in 3-space. Curvature and torsion of space curves, Gaussian curvature of surfaces, the Theorema Egregium of Gauss. Offered occasionally. Three credit hours. MATH 4550: Nonlinear Dynamics and Chaos Bifurcation in one-dimensional flows. Two-dimensional flows, fixed points and linearization, conservative systems, index theory, limit cycles. Poincaré-Bendixson theory, bifurcations. Chaos, the Lorenz equation, discrete maps, fractals, and strange attractors. Prerequisite: MATH 3550: Differential Equations. Three credit hours.

MATH 4570: Partial Differential Equations Fourier series, Fourier Integrals, the heat equation, Staum-Liouville problems, the wave equation, the potential equation, problems in several dimensions, Laplace transforms numerical methods. Prerequisite: MATH 3550: Differential Equations. Three credit hours.

MATH 4630: Graph Theory Basic definitions and concepts, undirected graphs (trees and graphs with cycles), directed graphs, and operation on graphs, Euler's formula, and surfaces. Offered occasionally. Prerequisite: MATH 2530: Calculus III. Three credit hours.

MATH 4650: Cryptography Classical cryptographic systems, public key cryptography, symmetric block ciphers, implementation issues. Related and supporting mathematical concepts and structures. Prerequisite: MATH 2530: Calculus III. Three credit hours. 

MATH 4800: Probability Theory Axioms of probability, conditional probability. Discrete and continuous random variables, expectation, jointly defined random variables. Transformations of random variables and limit theorems. Theory and applications, taught using statistical software. Credit not given for any two of MATH 3800, MATH 4800 and MATH 4810. Prerequisites: MATH/STAT 3850, MATH 2530 and MATH 1660 or MATH 2660. Three credit hours.

MATH 4840: Time Series Applied time series. Topics include exploratory data analysis, regression, ARIMA. Spectral analysis, state- space models. Theory and applications, taught using statistical software. Prerequisite: MATH/STAT 3850. Three credit hours.

MATH 4850: Mathematical Statistics Theory of estimators, sampling distributions, hypothesis testing, confidence intervals, regression, bootstrapping, and resampling. Theory and applications, taught using statistical software. Credit not given for both MATH/STAT 3810 and MATH/STAT 3850. Prerequisite: MATH 4800. Three credit hours.

MATH 4860: Statistical Models Poisson processes, Markov chains, hidden Markov models, continuous time Markov chains, queuing theory. Theory and applications, taught with statistical software. Prerequisite: MATH 4800 . Three credit hours.

MATH 4870: Applied Regression Linear regression, model selection, nonparametric regression, classification and graphical models. Theory and applications using statistical software. Prerequisites: MATH/STAT 3850 and MATH 3110 or MATH 3120. Three credit hours.

MATH 4950: Senior Residency Required for graduating seniors. 0 Credit Hours. Senior Residency

MATH 4980: Advanced Independent Study Prior permission of sponsoring professor and chair required. Zero to six credit hours. Independent Study.

MATH 4WUI - Washington University Inter-U 0 to 3 Credit Hours. Inter-University College

Graduate Courses

MATH 5102: Linear Algebra Advanced linear algebra including linear transformations and duality, elementary canonical forms, rational and Jordan forms, inner product spaces, unitary operators, normal operators, and spectral theory. Offered every other spring semester. Prerequisite: MATH 4110. Three credit hours. (Cross-listed as MATH 4120)

MATH 5202: Metric Spaces Set theory, real line, separation properties, compactness, metric spaces, metrization. Offered every other spring semester. Prerequisite: MATH 4210. Three credit hours. (Cross-listed as MATH 4220)

MATH 5105: Number Theory Introduction to algebraic number theory. Topics will include primes, Chinese remainder theorem, Diophantine equations, algebraic numbers and quadratic residues. Additional topics will vary from year to year. Offered every other year. Prerequisite: MATH 4110. Three credit hours. (Cross-listed as MATH 4150)

MATH 5203: Multivariable Analysis Sequences and Series of functions, Differentiability, Integrability, Inverse and Implicit function theorems, Fundamental Theorems of Multi-variable Calculus (Green’s Theorem, Stokes Theorem, Divergence Theorem). Prerequisite: MATH 4210. Three credit hours. (Cross-listed as MATH 4230)

MATH 5060: Math Methods Engineering I Review of vector analysis, curvilinear coordinates, introduction to partial differential equations, Cartesian tensors, matrices, similarity transformations, variational methods, Lagrange multipliers, Cauchy-Riemann conditions, geometry of a complex plane, conformal mapping, and engineering applications. Only offered occasionally. Prerequisite: Permission of Instructor. Three credit hours.

MATH 5070: Math Methods Engineering II Calculus of residues, contour integration, multi-valued functions, series solutions of differential equations, Sturm-Liouville theory, special functions, integral transforms, discrete Laplace and Fourier transforms, basic numerical methods, finite difference methods, and their applications to partial differential equations. Only offered occasionally. Prerequisite: Permission of Instructor. Three credit hours.

MATH 5110: Algebra Simple properties of groups, groups of transformations,subgroups, homomorphisms and isomorphisms, theorems of Schreier and Jordan-Hölder, mappings into a group, rings, integral domains, fields, polynomials, direct sums and modules. Fall semester. Three credit hours.

MATH 5120: Algebra II Rings, fields, bases and degrees of extension fields, transcendental elements, normal fields and their structures. Galois theory, finite fields; solutions of equations by radicals, general equations of degree n. Offered every spring semester. Prerequisite: MATH 5110. 3 Credit Hours.

MATH 5210: Real Analysis I The topology of the reals, Lebesque and Borel measurable functions, properties of the Lebesque integral, differential of the integral. Fall semester. Three credit hours.

MATH 5220: Complex Analysis Holomorphic and Harmonic functions and power series expansions. Complex integration. Cauchy’s theorem and applications. Laurent series, singularities, Runge’s theorem, and the calculus of residues. Additional topics may include Analytic continuation, Riemann surfaces, and conformal mapping. Prerequisite: MATH 5210 and MATH 5310. Three credit hours. Offered occasionally.

MATH 5230: Functional Analysis Banach and Hilbert spaces. Linear functionals and linear operators. Dual spaces, weak and weak-* topologies. Hahn-Banach, Closed Graph and Open Mapping Theorems. Topological Vector spaces. Prerequisite: MATH 5210 and MATH 5310. Three credit hours. Offered occasionally.

MATH 5240: Harmonic Analysis Fourier Series on the circle, Convergence of Fourier series, Conjugate and maximal functions, Interpolation of Linear Operators, Lacunary Sequences, Fourier Transform on the line, Fourier transform on locally compact Abelian groups. Prerequisite: MATH 5210. Three credit hours. Offered occasionally.

MATH 5310: Topology I Topological spaces, convergence, nets, product spaces, metrization, compact spaces, connected spaces. Fall semester. Three credit hours.

MATH 5320: Topology II Compact surfaces, fundamental groups, force groups and free products, Seifert-van Kampen theorem, covering spaces. Offered every spring semester. Prerequisite: MATH 5310. Three credit hours.

MATH 5930: Special Topics in Mathematics One to three credit hours. Graduate.

MATH 5950: Special Study for Examinations Zero Credit Hours. Graduate Special Study Exams.

MATH 5980: Graduate Reading Course Prior permission of instructor and chairperson required. One to three credit hours. Graduate independent study

MATH 5990: Thesis Research Zero to six credit hours. Graduate research.

MATH 5CR: Master’s Degree Study Zero credit hours. Graduate research.

MATH 5WUI: Washington University Inter-University Course Zero to three credit hours. Graduate.

MATH 6110: Algebra III Categories and functors, properties of hom and tensor, projective and injective modules, chain conditions, decomposition and cancellation of modules, theorems of Maschke, Wedderburn, and Artin-Wedderburn, tensor algebras. Offered occasionally. Three credit hours.

MATH 6180: Topics in Algebra Various topics are discussed to bring graduate students to the forefront of a research area in algebra. Times of offering in accordance with research interests of faculty. Offered occasionally. Three credit hours.

MATH 6210: Lie Groups and Lie Algebras Lie groups and Lie algebras, matrix groups, the Lie algebra of a Lie group, homogeneous spaces, solvable and nilpotent groups, semisimple Lie groups. Offered every other year. Three credit hours.

MATH 6220: Representation Theory of Lie Groups Representation theory of Lie groups, irreducibility and complete reducibility, Cartan subalgebra and root space decomposition, root system and classification, coadjoint orbits, harmonic analysis on homogeneous spaces. Offered every other year. Three credit hours.

MATH 6280: Topics in Analysis Various topics are offered to bring graduate students to the forefront of a research area in analysis. Times of offering in accordance with research interests of faculty. Offered occasionally. Three credit hours.

MATH 6310: Algebraic Topology Homotopy theory, homology theory, exact sequences, Mayer-Victoris sequences, degrees of maps, cohomology, Kunneth formula, cup and cap products, applications to manifolds including Poincare-Lefshetz duality. Offered every other year. Three credit hours.

MATH 6320: Topology of Manifolds Examples of manifolds, the tangent bundle, maps between manifolds, embeddings, critical values, transversality, isotopies, vector bundles and bubular neighborhoods, cobordism, intersection numbers and Euler characteristics. May be taught in either the piecewise linear or differentiable categories. Offered every other year. Three credit hours.

MATH 6380: Topics in Topology Various topics are offered to bring graduate students to the forefront of a research area in topology. Times of offering in accordance with research interests of faculty. Offered occasionally. Three credit hours.

MATH 6410: Differential Geometry I The theory of differentiable manifolds, topological manifolds, differential calculus of several variables, smooth manifolds and submanifolds, vector fields and ordinary differential equations, tensor fields, integration and de Rham cohomology. Fall semester. Three credit hours.

MATH 6420: Differential Geometry II Continuation of MATH 641. Offered every spring semester. Three credit hours.

MATH 6480: Topics in Geometry Various topics are offered to bring graduate students to the forefront of a research area in geometry. Times of offering in accordance with research interests of faculty. Offered occasionally. Three credit hours.

MATH 6950: Special Study for Examinations Zero credit hours. Graduate special study exams.

MATH 6980: Graduate Reading Course Prior permission of instructor and chairperson required. One to three credit hours. Graduate Independent study.

MATH 6990: Dissertation Research Zero to six credit hours. Graduate Research.

MATH 6CR: Doctor of Philosophy Degree Study Zero credit hours. Graduate.

SPH Snapshot: Summer Send-off

Income, Urbanicity Influence Perceptions of Factors that Shape Health

A clear path through murky waters: alum finds meaningful career studying water contamination ..

Beth Haley (SPH’24) during an early attempt at foraging for mushrooms in Oregon. During this trip, she learned these mushrooms were not edible, which she happily figured out before tasting them.

A Clear Path through Murky Waters: Alum Finds Meaningful Career Studying Water Contamination

Beth Haley’s PhD dissertation in environmental health linked sewage overflows with illness in Massachusetts and now her current post-doctoral research with the Environmental Protection Agency aims to tackle water quality in Pacific coastal areas.

Megan jones.

Upon finishing her PhD in environmental health at the School of Public Health, Beth Haley (SPH’24) moved to Oregon, drawn, she says, to the vast natural landscapes more commonly found out West. As a post-doctoral researcher with the Environmental Protection Agency (EPA), Haley aims to tackle threats to water quality specific to the Pacific Northwest.

“There are a lot of intact ecosystems here and the connection is, in some ways, even stronger between human communities and natural communities,” says Haley, whose dissertation work at SPH laid the foundation for her growing expertise at the intersection of water and public health. Haley and her advisor Wendy Heiger-Bernays , clinical professor of environmental health, recently published the results of a study Haley led linking overflows of sewage systems that combine wastewater and stormwater drainage with gastrointestinal illness in communities along the Merrimack River in Massachusetts.

Haley grew up on the North Shore of Massachusetts, earned her bachelor’s degree in conservation biology from Boston University, then lived in Colorado and New Mexico for eight years. She held several research positions that enabled her to explore her interest in ecology before she pivoted to working full-time for a TEDx program in Albuquerque, N.M. There, she found herself most inspired by the speakers whose work applied science in service of communities, she says.

“There are a lot of issues in ecology and conservation where there is an ethical gray area, where there are a lot of complicating factors and it can be difficult to discern right and wrong,” says Haley, who, in the years after college, found herself reevaluating her relationship with her field. For example, a traditional Western approach to conservation of endangered species often advocates for reducing the human footprint on an animal’s environment, such as by restricting hunting, she says. However, indigenous people have frequently coexisted with wildlife in these habits for generations, employing their own methods of land stewardship. Determined to serve both natural ecosystems and human communities in her career, Haley found that the sustainable management of water in support of human and non-human communities offered greater clarity.

“Water quality and access to water are issues where I feel there is no gray area,” she says. “It is very ethically black and white, and from an ecological standpoint, clean water used to be much more readily accessible before anthropogenic changes to land use and pollution. When an ecosystem has a lot of integrity, the water in rivers and lakes is generally quite clean.”

Bolstered by her belief that access to clean water is a human right, Haley sought a program of advanced study that would integrate her passions for ecology, human health, water quality, and climate change.  “The Boston University URBAN program stood out,” she says.

In 2018, Haley joined the first cohort of students to embark on their PhD studies through Boston University’s Graduate Program in Urban Biogeoscience and Environmental Health (URBAN) . The interdisciplinary degree program aims to equip professionals with the science, management, policy, communication, and governance skills necessary for collaborating with governments, non-profits, and the private sector to address urban environmental challenges.

Haley discussed her experience participating in the BU URBAN program as an EH student, and how she is applying her education to her post-doctoral research in Oregon.

With Beth Haley (SPH‘24)

Did you go into the BU URBAN program knowing you were going to study combined sewage overflows (CSO)? How did you come up with that project?

I knew that I wanted to work with Dr. Heiger-Bernays because she studies a lot of different water-related issues, but [I] did not have a specific project in mind. I remember in my first year we were talking, and she said, ‘You know, there is something going on in the Merrimack,’ and we started talking about CSOs. [They are] interesting as a public health issue because we have known for a very long time that when people are exposed to sewage, they tend to get sick—that is a pretty straightforward relationship—but combined sewers still exist in our communities, especially because they are such large systems that are so expensive to change, and have not actually been studied that much in terms of their relationship with health. A lot of these [combined] sewers were built when sewer systems were new in this country in the first place, and the design is no longer used for new systems. When some of them were built, germ theory was not even widely accepted. There were bigger perhaps or more visible issues at the time than whether there was pollution in the river. We have so many issues with water infrastructure in this country—it seemed like contributing to that literature could be beneficial to decisionmakers.

Could you provide an example of a place where these systems have been retrofitted?

Boston is a good example. One of the ways to reduce the number of overflow events is to introduce a lot of storage into the system. The pipes just receive a ton of volume of water during heavy rain events, so if you can take a bunch of that water and just store it until it stops raining, then later on you can slowly send that to the wastewater treatment plant to be treated. One of the things Boston has done is put a very large storage facility in South Boston, below ground, that has reduced a lot of the overflow events that used to happen in those South Boston and Dorchester beaches. That has cleaned up the water quite a bit.

Another way people have managed [CSOs] is to introduce more green stormwater infrastructure into cities. Putting in things like rain gardens that collect rainfall and allow it to infiltrate into the soil, mimicking natural processes, can help reduce some of that stormwater runoff volume in the first place.

Before you took your current position with EPA, you worked as an ORISE postdoctoral fellow with the U.S. Forest Service . Could you share what your research there entailed?

During my ORISE postdoc with the Forest Service, I was part of an interdisciplinary project focused on wildfire and water security project. [After wildfires,] there is often a lot of erosion and runoff from burned landscapes that complicates drinking water treatment processes. We are in the early stages of understanding on how wildfires impact water quality and drinking water treatment and how that varies over different landscapes, different burn severities, things like that. When wildfires impact distribution systems or other built infrastructure directly, you can also get a lot of chemicals that hang around in the water system at that point. The team is very interdisciplinary with hydrologist, watershed modelers, biologists, and environmental economists who are thinking about this issue of wildfire and water security from the perspective of communities and ecosystems. I contributed specifically to projects looking at the human dimensions of wildfire and water issues that are especially relevant for communities and drinking water utilities.

This project was motivated by the 2020 fires in Oregon. Around Labor Day in 2020, there were a number of very intense and large fires in western Oregon, which is where most of the population in Oregon lives, that impacted some watersheds that provide drinking water for some of the cities in that area. It drew a lot of attention to this issue, especially in Oregon and in the Pacific Northwest. Much of the research that has been done on drinking water impacts from wildfire had been done in more of the Intermountain West , like Colorado, as well as California, so there was a gap in the Pacific Northwest, and it is looking like those Pacific Northwest watersheds vary in how they behave compared to the Intermountain West systems.

And what is the focus of your new role with EPA?

Every five years or so, the EPA will offer these federal post docs where you are actually a federal employee for your term. They can be a little bit longer than ORISE positions, and you can invest more as an employee. I began on June 2 and will be in this position for three years. I am in the Pacific Coastal Ecology Branch (PCEB) and so my focus is to connect some of the coastal, marine, and estuarine ecology research that has been done here with human with human health and wellbeing outcomes. We are thinking about things like contaminants in water and shellfish, harmful agal blooms—we are talking about a lot of ideas right now. The work we do will fit within the overall priorities of the [EPA] Office of Research and Development and bring in more of that connection between ecosystem health and human health.

I am also going to carry over some of the projects I was working on with the Forest Service and continue contributing to those. My time with the Forest Service was really wonderful. I would not have necessarily made this jump to EPA had this opportunity not been so in line with my research interests. The federal agency postdoc world is a very specific set of opportunities, so it has also been interesting to learn about that and experience the differences between different kinds of positions.

[Wendy Heiger-Bernays and I] are still working on some projects too. We have one dissertation paper that still needs to be published, hopefully. Then, we have two side projects that I did not get to as part of my dissertation, but other BUSPH students have contributed to those efforts and we are working towards finishing those as well. One of them is a modeling project, led by Talia Feldscher (SPH’23), a research data analyst with the Center for Climate and Health, working on developing a model that will predict E. coli concentrations in the Merrimack [River]. The other uses a risk assessment approach to understand the risk of gastrointestinal illness for people who are recreating in the Merrimack, and recent MPH graduate Emily Gant (SPH’24) has been working with us on that project. The nature of a post doc is you have some unfinished projects from previous experiences.

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Using Bayesian Occupancy Modeling to Inform Bat Conservation in Indiana, Sally Martinez Master's Thesis Defense

Please join us June 26 th  at 2:00 pm to support Sally Martinez as she defends her thesis Using Bayesian Occupancy Modeling to Inform Bat Conservation in Indiana. We hope to see you there in FORS 208 or online on Zoom .

Faculty Advisor: Dr. Patrick Zollner

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Presentation Master's Thesis - Jody Kamper- Developmental psychology

Roeterseilandcampus - Gebouw G, Straat: Nieuwe Achtergracht 129-B, Ruimte: GS.05

This thesis investigates the role of age in the relationship between  social attunement, social drinking motives and (problematic) alcohol use. Using the Social Attunement Questionnaire (SAQ), the study examines how individuals adjust their behavior and thoughts to align with social expectations, exploring its impact on social drinking motives and (problematic) alcohol use.

A diverse sample of 502 participants aged 16 to 60 from the Netherlands was recruited through social media and university networks. Participants completed comprehensive questionnaires assessing their social attunement levels, social drinking motives (measured by the DMQ-R), and alcohol use patterns (evaluated using the TLFB and AUDIT). This study aims to deepen understanding of the mechanisms through which social attunement may lead to problematic alcohol use, providing insights that could inform targeted interventions.