phd thesis statistics

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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How To Write The Results/Findings Chapter

For quantitative studies (dissertations & theses).

By: Derek Jansen (MBA) | Expert Reviewed By: Kerryn Warren (PhD) | July 2021

So, you’ve completed your quantitative data analysis and it’s time to report on your findings. But where do you start? In this post, we’ll walk you through the results chapter (also called the findings or analysis chapter), step by step, so that you can craft this section of your dissertation or thesis with confidence. If you’re looking for information regarding the results chapter for qualitative studies, you can find that here .

Overview: Quantitative Results Chapter

• What exactly the results chapter is
• What you need to include in your chapter
• How to structure the chapter
• Tips and tricks for writing a top-notch chapter
• Free results chapter template

What exactly is the results chapter?

The results chapter (also referred to as the findings or analysis chapter) is one of the most important chapters of your dissertation or thesis because it shows the reader what you’ve found in terms of the quantitative data you’ve collected. It presents the data using a clear text narrative, supported by tables, graphs and charts. In doing so, it also highlights any potential issues (such as outliers or unusual findings) you’ve come across.

But how’s that different from the discussion chapter?

Well, in the results chapter, you only present your statistical findings. Only the numbers, so to speak – no more, no less. Contrasted to this, in the discussion chapter , you interpret your findings and link them to prior research (i.e. your literature review), as well as your research objectives and research questions . In other words, the results chapter presents and describes the data, while the discussion chapter interprets the data.

Let’s look at an example.

In your results chapter, you may have a plot that shows how respondents to a survey  responded: the numbers of respondents per category, for instance. You may also state whether this supports a hypothesis by using a p-value from a statistical test. But it is only in the discussion chapter where you will say why this is relevant or how it compares with the literature or the broader picture. So, in your results chapter, make sure that you don’t present anything other than the hard facts – this is not the place for subjectivity.

It’s worth mentioning that some universities prefer you to combine the results and discussion chapters. Even so, it is good practice to separate the results and discussion elements within the chapter, as this ensures your findings are fully described. Typically, though, the results and discussion chapters are split up in quantitative studies. If you’re unsure, chat with your research supervisor or chair to find out what their preference is.

What should you include in the results chapter?

Following your analysis, it’s likely you’ll have far more data than are necessary to include in your chapter. In all likelihood, you’ll have a mountain of SPSS or R output data, and it’s your job to decide what’s most relevant. You’ll need to cut through the noise and focus on the data that matters.

This doesn’t mean that those analyses were a waste of time – on the contrary, those analyses ensure that you have a good understanding of your dataset and how to interpret it. However, that doesn’t mean your reader or examiner needs to see the 165 histograms you created! Relevance is key.

How do I decide what’s relevant?

At this point, it can be difficult to strike a balance between what is and isn’t important. But the most important thing is to ensure your results reflect and align with the purpose of your study .  So, you need to revisit your research aims, objectives and research questions and use these as a litmus test for relevance. Make sure that you refer back to these constantly when writing up your chapter so that you stay on track.

As a general guide, your results chapter will typically include the following:

• Some demographic data about your sample
• Reliability tests (if you used measurement scales)
• Descriptive statistics
• Inferential statistics (if your research objectives and questions require these)
• Hypothesis tests (again, if your research objectives and questions require these)

We’ll discuss each of these points in more detail in the next section.

Importantly, your results chapter needs to lay the foundation for your discussion chapter . This means that, in your results chapter, you need to include all the data that you will use as the basis for your interpretation in the discussion chapter.

For example, if you plan to highlight the strong relationship between Variable X and Variable Y in your discussion chapter, you need to present the respective analysis in your results chapter – perhaps a correlation or regression analysis.

Need a helping hand?

How do I write the results chapter?

There are multiple steps involved in writing up the results chapter for your quantitative research. The exact number of steps applicable to you will vary from study to study and will depend on the nature of the research aims, objectives and research questions . However, we’ll outline the generic steps below.

Step 1 – Revisit your research questions

The first step in writing your results chapter is to revisit your research objectives and research questions . These will be (or at least, should be!) the driving force behind your results and discussion chapters, so you need to review them and then ask yourself which statistical analyses and tests (from your mountain of data) would specifically help you address these . For each research objective and research question, list the specific piece (or pieces) of analysis that address it.

At this stage, it’s also useful to think about the key points that you want to raise in your discussion chapter and note these down so that you have a clear reminder of which data points and analyses you want to highlight in the results chapter. Again, list your points and then list the specific piece of analysis that addresses each point. 

Next, you should draw up a rough outline of how you plan to structure your chapter . Which analyses and statistical tests will you present and in what order? We’ll discuss the “standard structure” in more detail later, but it’s worth mentioning now that it’s always useful to draw up a rough outline before you start writing (this advice applies to any chapter).

Step 2 – Craft an overview introduction

As with all chapters in your dissertation or thesis, you should start your quantitative results chapter by providing a brief overview of what you’ll do in the chapter and why . For example, you’d explain that you will start by presenting demographic data to understand the representativeness of the sample, before moving onto X, Y and Z.

This section shouldn’t be lengthy – a paragraph or two maximum. Also, it’s a good idea to weave the research questions into this section so that there’s a golden thread that runs through the document.

Step 3 – Present the sample demographic data

The first set of data that you’ll present is an overview of the sample demographics – in other words, the demographics of your respondents.

For example:

• What age range are they?
• How is gender distributed?
• How is ethnicity distributed?
• What areas do the participants live in?

The purpose of this is to assess how representative the sample is of the broader population. This is important for the sake of the generalisability of the results. If your sample is not representative of the population, you will not be able to generalise your findings. This is not necessarily the end of the world, but it is a limitation you’ll need to acknowledge.

Of course, to make this representativeness assessment, you’ll need to have a clear view of the demographics of the population. So, make sure that you design your survey to capture the correct demographic information that you will compare your sample to.

But what if I’m not interested in generalisability?

Well, even if your purpose is not necessarily to extrapolate your findings to the broader population, understanding your sample will allow you to interpret your findings appropriately, considering who responded. In other words, it will help you contextualise your findings . For example, if 80% of your sample was aged over 65, this may be a significant contextual factor to consider when interpreting the data. Therefore, it’s important to understand and present the demographic data.

 Step 4 – Review composite measures and the data “shape”.

Before you undertake any statistical analysis, you’ll need to do some checks to ensure that your data are suitable for the analysis methods and techniques you plan to use. If you try to analyse data that doesn’t meet the assumptions of a specific statistical technique, your results will be largely meaningless. Therefore, you may need to show that the methods and techniques you’ll use are “allowed”.

Most commonly, there are two areas you need to pay attention to:

#1: Composite measures

The first is when you have multiple scale-based measures that combine to capture one construct – this is called a composite measure .  For example, you may have four Likert scale-based measures that (should) all measure the same thing, but in different ways. In other words, in a survey, these four scales should all receive similar ratings. This is called “ internal consistency ”.

Internal consistency is not guaranteed though (especially if you developed the measures yourself), so you need to assess the reliability of each composite measure using a test. Typically, Cronbach’s Alpha is a common test used to assess internal consistency – i.e., to show that the items you’re combining are more or less saying the same thing. A high alpha score means that your measure is internally consistent. A low alpha score means you may need to consider scrapping one or more of the measures.

#2: Data shape

The second matter that you should address early on in your results chapter is data shape. In other words, you need to assess whether the data in your set are symmetrical (i.e. normally distributed) or not, as this will directly impact what type of analyses you can use. For many common inferential tests such as T-tests or ANOVAs (we’ll discuss these a bit later), your data needs to be normally distributed. If it’s not, you’ll need to adjust your strategy and use alternative tests.

To assess the shape of the data, you’ll usually assess a variety of descriptive statistics (such as the mean, median and skewness), which is what we’ll look at next.

Step 5 – Present the descriptive statistics

Now that you’ve laid the foundation by discussing the representativeness of your sample, as well as the reliability of your measures and the shape of your data, you can get started with the actual statistical analysis. The first step is to present the descriptive statistics for your variables.

For scaled data, this usually includes statistics such as:

• The mean – this is simply the mathematical average of a range of numbers.
• The median – this is the midpoint in a range of numbers when the numbers are arranged in order.
• The mode – this is the most commonly repeated number in the data set.
• Standard deviation – this metric indicates how dispersed a range of numbers is. In other words, how close all the numbers are to the mean (the average).
• Skewness – this indicates how symmetrical a range of numbers is. In other words, do they tend to cluster into a smooth bell curve shape in the middle of the graph (this is called a normal or parametric distribution), or do they lean to the left or right (this is called a non-normal or non-parametric distribution).
• Kurtosis – this metric indicates whether the data are heavily or lightly-tailed, relative to the normal distribution. In other words, how peaked or flat the distribution is.

A large table that indicates all the above for multiple variables can be a very effective way to present your data economically. You can also use colour coding to help make the data more easily digestible.

For categorical data, where you show the percentage of people who chose or fit into a category, for instance, you can either just plain describe the percentages or numbers of people who responded to something or use graphs and charts (such as bar graphs and pie charts) to present your data in this section of the chapter.

When using figures, make sure that you label them simply and clearly , so that your reader can easily understand them. There’s nothing more frustrating than a graph that’s missing axis labels! Keep in mind that although you’ll be presenting charts and graphs, your text content needs to present a clear narrative that can stand on its own. In other words, don’t rely purely on your figures and tables to convey your key points: highlight the crucial trends and values in the text. Figures and tables should complement the writing, not carry it .

Depending on your research aims, objectives and research questions, you may stop your analysis at this point (i.e. descriptive statistics). However, if your study requires inferential statistics, then it’s time to deep dive into those .

Step 6 – Present the inferential statistics

Inferential statistics are used to make generalisations about a population , whereas descriptive statistics focus purely on the sample . Inferential statistical techniques, broadly speaking, can be broken down into two groups .

First, there are those that compare measurements between groups , such as t-tests (which measure differences between two groups) and ANOVAs (which measure differences between multiple groups). Second, there are techniques that assess the relationships between variables , such as correlation analysis and regression analysis. Within each of these, some tests can be used for normally distributed (parametric) data and some tests are designed specifically for use on non-parametric data.

There are a seemingly endless number of tests that you can use to crunch your data, so it’s easy to run down a rabbit hole and end up with piles of test data. Ultimately, the most important thing is to make sure that you adopt the tests and techniques that allow you to achieve your research objectives and answer your research questions .

In this section of the results chapter, you should try to make use of figures and visual components as effectively as possible. For example, if you present a correlation table, use colour coding to highlight the significance of the correlation values, or scatterplots to visually demonstrate what the trend is. The easier you make it for your reader to digest your findings, the more effectively you’ll be able to make your arguments in the next chapter.

Step 7 – Test your hypotheses

If your study requires it, the next stage is hypothesis testing. A hypothesis is a statement , often indicating a difference between groups or relationship between variables, that can be supported or rejected by a statistical test. However, not all studies will involve hypotheses (again, it depends on the research objectives), so don’t feel like you “must” present and test hypotheses just because you’re undertaking quantitative research.

The basic process for hypothesis testing is as follows:

• Specify your null hypothesis (for example, “The chemical psilocybin has no effect on time perception).
• Specify your alternative hypothesis (e.g., “The chemical psilocybin has an effect on time perception)
• Set your significance level (this is usually 0.05)
• Calculate your statistics and find your p-value (e.g., p=0.01)
• Draw your conclusions (e.g., “The chemical psilocybin does have an effect on time perception”)

Finally, if the aim of your study is to develop and test a conceptual framework , this is the time to present it, following the testing of your hypotheses. While you don’t need to develop or discuss these findings further in the results chapter, indicating whether the tests (and their p-values) support or reject the hypotheses is crucial.

Step 8 – Provide a chapter summary

To wrap up your results chapter and transition to the discussion chapter, you should provide a brief summary of the key findings . “Brief” is the keyword here – much like the chapter introduction, this shouldn’t be lengthy – a paragraph or two maximum. Highlight the findings most relevant to your research objectives and research questions, and wrap it up.

Some final thoughts, tips and tricks

Now that you’ve got the essentials down, here are a few tips and tricks to make your quantitative results chapter shine:

• When writing your results chapter, report your findings in the past tense . You’re talking about what you’ve found in your data, not what you are currently looking for or trying to find.
• Structure your results chapter systematically and sequentially . If you had two experiments where findings from the one generated inputs into the other, report on them in order.
• Make your own tables and graphs rather than copying and pasting them from statistical analysis programmes like SPSS. Check out the DataIsBeautiful reddit for some inspiration.
• Once you’re done writing, review your work to make sure that you have provided enough information to answer your research questions , but also that you didn’t include superfluous information.

If you’ve got any questions about writing up the quantitative results chapter, please leave a comment below. If you’d like 1-on-1 assistance with your quantitative analysis and discussion, check out our hands-on coaching service , or book a free consultation with a friendly coach.

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Thank you. I will try my best to write my results.

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this was great explaination

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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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Home > Statistics > Dissertations, Theses, and Student Work

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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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Cornell University does not offer a separate Masters of Science (MS) degree program in the field of Statistics. Applicants interested in obtaining a masters-level degree in statistics should consider applying to Cornell's MPS Program in Applied Statistics.

Choosing a Field of Study

There are many graduate fields of study at Cornell University. The best choice of graduate field in which to pursue a degree depends on your major interests. Statistics is a subject that lies at the interface of theory, applications, and computing. Statisticians must therefore possess a broad spectrum of skills, including expertise in statistical theory, study design, data analysis, probability, computing, and mathematics. Statisticians must also be expert communicators, with the ability to formulate complex research questions in appropriate statistical terms, explain statistical concepts and methods to their collaborators, and assist them in properly communicating their results. If the study of statistics is your major interest then you should seriously consider applying to the Field of Statistics.

There are also several related fields that may fit even better with your interests and career goals. For example, if you are mainly interested in mathematics and computation as they relate to modeling genetics and other biological processes (e.g, protein structure and function, computational neuroscience, biomechanics, population genetics, high throughput genetic scanning), you might consider the Field of Computational Biology . You may wish to consider applying to the Field of Electrical and Computer Engineering if you are interested in the applications of probability and statistics to signal processing, data compression, information theory, and image processing. Those with a background in the social sciences might wish to consider the Field of Industrial and Labor Relations with a major or minor in the subject of Economic and Social Statistics. Strong interest and training in mathematics or probability might lead you to choose the Field of Mathematics . Lastly, if you have a strong mathematics background and an interest in general problem-solving techniques (e.g., optimization and simulation) or applied stochastic processes (e.g., mathematical finance, queuing theory, traffic theory, and inventory theory) you should consider the Field of Operations Research .

Residency Requirements

Students admitted to PhD program must be "in residence" for at least four semesters, although it is generally expected that a PhD will require between 8 and 10 semesters to complete. The chair of your Special Committee awards one residence unit after the satisfactory completion of each semester of full-time study. Fractional units may be awarded for unsatisfactory progress.

Your Advisor and Special Committee

The Director of Graduate Studies is in charge of general issues pertaining to graduate students in the field of Statistics. Upon arrival, a temporary Special Committee is also declared for you, consisting of the Director of Graduate Studies (chair) and two other faculty members in the field of Statistics. This temporary committee shall remain in place until you form your own Special Committee for the purposes of writing your doctoral dissertation. The chair of your Special Committee serves as your primary academic advisor; however, you should always feel free to contact and/or chat with any of the graduate faculty in the field of Statistics.

The formation of a Special Committee for your dissertation research should serve your objective of writing the best possible dissertation. The Graduate School requires that this committee contain at least three members that simultaneously represent a certain combination of subjects and concentrations. The chair of the committee is your principal dissertation advisor and always represents a specified concentration within the subject & field of Statistics. The Graduate School additionally requires PhD students to have at least two minor subjects represented on your special committee. For students in the field of Statistics, these remaining two members must either represent (i) a second concentration within the subject of Statistics, and one external minor subject; or, (ii) two external minor subjects. Each minor advisor must agree to serve on your special committee; as a result, the identification of these minor members should occur at least 6 months prior to your A examination.

Some examples of external minors include Computational Biology, Demography, Computer Science, Economics, Epidemiology, Mathematics, Applied Mathematics and Operations Research. The declaration of an external minor entails selecting (i) a field other than Statistics in which to minor; (ii) a subject & concentration within the specified field; and, (iii) a minor advisor representing this field/subject/concentration that will work with you in setting the minor requirements. Typically, external minors involve gaining knowledge in 3-5 graduate courses in the specified field/subject, though expectations can vary by field and even by the choice of advisor. While any choice of external minor subject is technically acceptable, the requirement that the minor representative serve on your Special Committee strongly suggests that the ideal choice(s) should share some natural connection with your choice of dissertation topic.

The fields, subjects and concentrations represented on your committee must be officially recognized by the Graduate School ; the Degrees, Subjects & Concentrations tab listed under each field of study provides this information. Information on the concentrations available for committee members chosen to represent the subject of Statistics can be found on the Graduate School webpage . 

Statistics PhD Travel Support

The Department of Statistics and Data Science has established a fund for professional travel for graduate students. The intent of the Department is to encourage travel that enhances the Statistics community at Cornell by providing funding for graduate students in statistics that will be presenting at conferences. Please review the Graduate Student Travel Award Policy website for more information. 

Completion of the PhD Degree

In addition to the specified residency requirements, students must meet all program requirements as outlined in Program Course Requirements and Timetables and Evaluations and Examinations, as well as complete a doctoral dissertation approved by your Special Committee. The target time to PhD completion is between 4 and 5 years; the actual time to completion varies by student.

Students should consult both the Guide to Graduate Study and Code of Legislation of the Graduate Faculty (available at www.gradschool.cornell.edu ) for further information on all academic and procedural matters pertinent to pursuing a graduate degree at Cornell University.

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Thesis Defense

Smd statistics thesis guide supplement, purpose of this document.

This document provides a guide for the structure and content of a Statistics PhD thesis document. Because thesis topics and methods vary greatly, the requirements for any given thesis may vary from the guidelines presented here as is required to facilitate coherent presentation. However, notwithstanding such exceptions, the structure and content provided below is the standard for a Statistics PhD thesis at the University of Rochester.

This document is meant to be a supplement to the general guidelines of the University of Rochester for preparation of a thesis (“Preparing Your Thesis: a Manual for Graduate Students”), which can be found at the website http://www.rochester.edu/Theses/ThesesManual.pdf , and which governs all theses at this university. This document does not supersede the general guidelines.

Overview of thesis contents

A thesis is a description and interpretation of the research conducted by the candidate that qualifies him/her for the degree of PhD.

Wherever possible (particularly the introductory and final chapters), the thesis should be written so that the material is accessible to those not working in the specialized area of research. Every member of the thesis examination committee should be able to understand the main ideas in the document as a whole, and the details of each section must be understandable to at least one committee member with the expertise to verify that its content is sound.

The document should be written in English with correct spelling and grammar. It is not the job of the committee to proof-read the text. Having the text of the thesis corrected and edited for clarity by a second person is acceptable and highly recommended. A committee member can refuse to accept a thesis with excessive grammatical or typographical errors.

There is no formal minimum or maximum length. The thesis must give an in-depth account of the background and the research question addressed, as well as a detailed description of the methods and results that is typically more specific than that found in the published literature.

Organization of the thesis

The manual titled “Preparing Your Thesis: a Manual for Graduate Students” outlines the overall structure of the thesis in terms of general formatting and required parts such as the Title Page, Abstract, etc. This manual should be consulted for specifications regarding these components. This manual, however, does not address the substantive chapters of the thesis. That guidance is provided herein.

A PhD thesis in Statistics is expected to involve the development of novel statistical methodology and/or provide important contributions to the theory of statistics. It should consist of original work of publishable quality that addresses a unified theme, as opposed to a collection of unrelated methodological developments. A Statistics PhD thesis will typically contain five chapters (although this may vary):

Chapter 1. Introduction

This chapter introduces the research problem and outlines the relevant background. While expansive details of all relevant published works should be avoided, this chapter should summarize all pertinent scientific literature to provide the information necessary for understanding what is currently known and how the thesis will contribute in an important way to expanding this knowledge. This chapter provides the requisite arguments to establish the importance of the problem as a statistical research topic. Often, example data from actual scientific studies are highly useful for motivating the research problem. The chapter should conclude by briefly summarizing the research approach to the thesis and the organization of the remaining chapters.

Chapters 2-4. Distinct Aspects of the Research

Each of these chapters typically addresses a distinct sub-problem related to the general theme of the dissertation. The mathematical development of the novel methodology should be presented in detail. New theorems and proofs (as well as relevant existing theorems) should be provided as necessary for analytical evaluation of the properties of the new methods. Simulation studies may be necessary to empirically evaluate the properties of these methods; the simulation designs should be described in sufficient detail to allow replication of the results by others. Comparisons should be made to existing methods, if any, for addressing the same research problem. Results of the evaluations should be clearly and thoroughly presented in figures and tables that are self-contained.

Example data from actual scientific studies should be used whenever possible (and applicable) to illustrate the utility of the new methodology.

Chapter 5. Conclusions and Future Work

The final chapter should discuss the research findings in a unified framework and provide an overall perspective for the reader, including limitations of the research and future work to be performed. It may be helpful to briefly recapitulate the state of the field at the outset of the research, summarize the main results of the thesis, explain how the current work provides an important contribution to existing knowledge, point out any limitations of the newly-developed methods, raise new questions that may have arisen out of the research, and propose future work to address existing gaps in knowledge.

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PhD in Econometrics and Statistics

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The Econometrics and Statistics Program provides foundational training in the science of learning from data towards solving business problems. Our students engage in extensive collaborative research on cutting-edge theory in Econometrics, Statistics and Machine Learning as well in applied research from a variety of fields within Booth (such as finance, marketing or economics).

Our program builds on a long tradition of research creativity and excellence at Booth.

Our PhD students become active members of the broad, interdisciplinary and intellectually stimulating Booth community. The program is ideal for students who wish to pursue an (academic) research career in data-rich disciplines, and who are motivated by applications (including but not limited to economics and business). As our PhD student, you will have a freedom to customize your program by combining courses at Booth (including business-specific areas such as marketing, finance or economics) with offerings at our partnering departments at the University of Chicago (Department of Statistics and Kenneth C. Griffin Department of Economics). You will acquire a solid foundation in both theory and practice (including learning theory, Bayesian statistics, causal inference or empirical asset pricing).

Our Distinguished Econometrics and Statistics Faculty

Chicago Booth’s Econometrics and Statistics faculty are committed to building strong collaborative relationships with doctoral students. We serve as research advisors and career mentors. Major areas of departmental research include: learning theory; causal inference; machine learning; Bayesian inference; decision theory; graphical models; high dimensional inference; and financial econometrics.

Bryon Aragam

Assistant Professor of Econometrics and Statistics and Robert H. Topel Faculty Scholar

Nabarun Deb

Assistant Professor of Econometrics and Statistics

Christian B. Hansen

Wallace W. Booth Professor of Econometrics and Statistics

Tetsuya Kaji

Associate Professor of Econometrics and Statistics and Richard Rosett Faculty Fellow

Mladen Kolar

Associate Professor of Econometrics and Statistics

Tengyuan Liang

Professor of Econometrics and Statistics and William Ladany Faculty Fellow

Nicholas Polson

Robert Law, Jr. Professor of Econometrics and Statistics

Veronika Rockova

Professor of Econometrics and Statistics, and James S. Kemper Faculty Scholar

Jeffrey R. Russell

Alper Family Professor of Econometrics and Statistics

Ekaterina (Katja) Smetanina

Assistant Professor of Econometrics and Statistics and Asness Junior Faculty Fellow

Panagiotis Toulis (Panos)

Associate Professor of Econometrics and Statistics, and John E. Jeuck Faculty Fellow

Dacheng Xiu

Professor of Econometrics and Statistics

Spotlight on Research

Econometrics and statistics research from our PhD students and faculty is often featured in the pages of Chicago Booth Review.

Is There a Ceiling for Gains in Machine-Learned Arbitrage?

In a recent paper by Chicago Booth’s Stefan Nagel and Dacheng Xiu and Booth PhD student Rui Da, findings suggest that there are limits to statistical arbitrage investment.

How (In)accurate Is Machine Learning?

Three Chicago Booth researchers quantify the likelihood of machine learning leading business executives astray.

Would You Trust a Machine to Pick a Vaccine?

"If we understand why a black-box method works, we can trust it more with our decisions, explains [Booth's] Ročková, one of the researchers trying to narrow the gap between what’s done in practice and what’s known in theory. "

Scholarly Publications

Our PhD students' research has been published in top journals including Econometrica, Journal of Royal Statistical Society, Journal of Econometrics, Neural Information Processing Systems and Journal of Machine Learning Research. Below is a recent list of publications and working papers authored by our PhD students. Modeling Tail Index with Autoregressive Conditional Pareto Model Zhouyu Shen, Yu Chen and Ruxin Shi, Journal of Business and Economic Statistics, (40) 2022 Online Learning to Transport via the Minimal Selection Principle Wenxuan Guo, YoonHaeng Hur, Tengyuan Liang, Chris Ryan, Proceedings of 35th Conference on Learning Theory (COLT), (178) 2022 FuDGE: A Method to Estimate a Functional Differential Graph in a High-Dimensional Setting Boxin Zhao, Samuel Wang and Mladen Kolar, Journal of Machine Learning Research, (23) 2022 Approximate Bayesian Computation via Classification Yuexi Wang, Tetsuya Kaji and Veronika Rockova, Journal of Machine Learning Research (In press), 2022 Reversible Gromov-Monge Sampler for Simulation-Based Inference YoonHaeng Hur, Wenxuan Guo and Tengyuan Liang, Journal of the American Statistical Association (R&R). 2021. Data Augmentation for Bayesian Deep Learning Yuexi Wang, Nicholas Polson and Vadim Sokolov, Bayesian Analysis (In press), 2022 Pessimism Meets VCG: Learning Dynamic Mechanism Design via Offline Reinforcement Learning Boxiang Lyu, Zhaoran Wang, Mladen Kolar and Zhuoran Yang, In Proceedings of the 39th International Conference on Machine Learning (ICML), (162) 2022 Optimal Estimation of Gaussian DAG Models Ming Gao, Wai Ming Tai and Bryon Aragam, International Conference on Artificial Intelligence and Statistics (AISTATS), (151) 2022 Multivariate Change Point Detection for Heterogeneous Series Yuxuan Guo, Ming Gao, and Xiaoling Lu, Neurocomputing, (510) 2022 Disentangling Autocorrelated Intraday Returns Rui Da and Dacheng Xiu, Journal of Econometrics (R&R), 2021 When Moving-Average Models Meet High-Frequency Data: Uniform Inference on Volatility Rui Da and Dacheng Xiu, Econometrica, (89) 2021 Efficient Bayesian Network Structure Learning via Local Markov Boundary Search Ming Gao and Bryon Aragam, Advances in Neural Information Processing Systems (NeurIPS), (34) 2021 Structure Learning in Polynomial Time: Greedy Algorithms, Bregman Information, and Exponential Families Goutham Rajendran, Bohdan Kivva, Ming Gao and Bryon Aragam, Advances in Neural Information Processing Systems (NeurIPS), (34) 2021 Variable Selection with ABC Bayesian Forests Yi Liu, Yuexi Wang and Veronika Rockova, Journal of the Royal Statistical Association: Series B, (83) 2021  A Polynomial-time Algorithm for Learning Non-parametric Causal Graphs Ming Gao, Yi Ding, and Bryon Aragam, Advances in Neural Information Processing System (NeurIPS), (33) 2020 Uncertainty Quantification for Sparse Deep Learning Yuexi Wang and Veronika Rockova, International Conference on Artificial Intelligence and Statistics (AISTATS), (2018) 2020 Direct Estimation of Differential Functional Graphical Models Boxin Zhao, Samuel Wang and Mladen Kolar, Advances in neural information processing systems (NeurIPS), (32) 2019

The Effects of Economic Uncertainty on Financial Volatility: A Comprehensive Investigation Chen Tong, Zhuo Huang, Tianyi Wang, and Cong Zhang, Journal of Empirical Finance (R&R), 2022

A Network of Support

Booth’s Econometrics and Statistics group has been partnering with several (data science and interdisciplinary) research centers and institutes that facilitate the translation of research into practice. Through these venues, our PhD students can foster a strong research community and find additional resources including elective courses, funding for collaborative student work, and seminars with world-renowned scholars.

Data Science Institute at the University of Chicago The Data Science Institute executes the University of Chicago’s bold, innovative vision of Data Science as a new discipline by advancing interdisciplinary research, partnerships with industry, government, and social impact organizations. Center for Applied Artificial Intelligence The Center for Applied AI incubates transformative projects that fundamentally shape how humans use AI to interact with each other and the world. The Center’s innovative research uses machine learning and behavioral science to investigate how AI can best be used to support human decision-making and improve society. Toyota Technological Institute at Chicago Toyota Technological Institute at Chicago (TTIC) is a philanthropically endowed academic computer science institute, dedicated to basic research and graduate education in computer science. Its mission is to achieve international impact through world-class research and education in fundamental computer science and information technology. The Institute is distinctive to the American educational scene in its unique combination of graduate education and endowed research.

The Becker Friedman Institute for Economics With a mission of turning evidence-based research into real-world impact, the Becker Friedman Institute brings together the University of Chicago’s economic community. Ideas are translated into accessible formats and shared with world leaders tasked with solving pressing economic problems. Committee on Quantitative Methods in Social, Behavioral and Health Sciences This is an interdisciplinary community of faculty and students interested in methodological research in relation to applications in social, behavioral, and health sciences. The goals are to create an intellectual niche, exchange research ideas, facilitate research collaborations, share teaching resources, enhance the training of students, and generate a collective impact on the University of Chicago campus and beyond. The Institute for Data, Econometrics, Algorithms, and Learning The Institute for Data, Econometrics, Algorithms, and Learning (IDEAL) is a multi-discipline (computer science, statistics, economics, electrical engineering, and operations research) and multi-institution (Northwestern University, Toyota Technological Institute at Chicago, and University of Chicago) collaborative institute that focuses on key aspects of the theoretical foundations of data science. The institute will support the study of foundational problems related to machine learning, high-dimensional data analysis and optimization in both strategic and non-strategic environments.

The Fama-Miller Center for Research in Finance Tasked with pushing the boundaries of research in finance, the Fama-Miller Center provides institutional structure and support for researchers in the field. James M. Kilts Center for Marketing The Kilts Center facilitates faculty and student research, supports innovations in the marketing curriculum, funds scholarships for MBA and PhD students, and creates engaging programs aimed at enhancing the careers of students and alumni.

Inside the Student Experience

Damian Kozbur, PhD ’14, says PhD students at Booth have the flexibility to work on risky problems that no one else has examined.

Video Transcript

Damian Kozbur, ’14: 00:01 I went to graduate school in order to develop econometrics tools in conjunction with machine-learning tools in conjunction with economic theory in order to do inference for economic parameters. When you work in high dimensional estimation and you're dealing with problems where the number of variables you're looking at can potentially be in the millions, there's no way to visualize what's going on. Demands now really require that you can handle huge datasets. There's something really satisfying about studying a problem and studying it well. I would say Booth is an excellent place to do it. You have the flexibility to work on really risky problems where you're trying to navigate this landscape that nobody's ever really looked at before. You have an opportunity to dig deeper. You have an opportunity to be rigorous. The faculty is there to help you. They're trying to figure out the same kinds of problems. Things that you figure out cannot always be visualized and it cannot always be easily understood. That doesn't necessarily mean that it's not practical or not useful.

Damian Kozbur, ’14: 01:08 There's an incredible explosion in terms of the amount of data we have on everything. There is an incredible explosion in terms of our understanding of high dimensional econometrics. If you're doing innovative work right now, it will have an impact.

Current Econometrics and Statistics Students

PhD students in econometrics and statistics apply statistical methods to a wide range of business problems, from the effectiveness of machine-learning tools to video-game preferences. Our graduates go on to work in high-profile institutions, generally in academia, finance, or data science.

Current Students

Y ifei Chen Rui Da

Chaoxing Dai

Wenxuan Guo

Shuo-Chieh Huang

Shunzhuang Huang So Won (Sowon) Jeong

Boxiang (Shawn) Lyu Edoardo Marcelli

Zhouyu Shen

Shengjun (Percy) Zhai

Current Students in Sociology and Business

Jacy Anthis

Program Expectations and Requirements

The Stevens Doctoral Program at Chicago Booth is a full-time program. Students generally complete the majority of coursework and examination requirements within the first two years of studies and begin work on their dissertation during the third year. For details, see General Examination Requirements by Area in the Stevens Program Guidebook below.

Download the 2023-2024 Guidebook!

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Doctor of Philosophy

The Doctor of Philosophy program in statistics prepares students for careers in university teaching and research or in government or industrial research. Students entering the program spend four semesters acquiring a basic background in probability, mathematical statistics, and applied statistics and take general examinations on these subjects. More specialized study follows with the thesis research, which usually begins in the third year. This research may be concentrated in any area of statistics or probability in which a faculty member is interested. Students also have the opportunity to gain experience in applied statistics through participation in statistical consulting . Completion of the Ph.D. program normally requires three to five years.

Requirements

Students who enter this program should have knowledge of probability equivalent to the content of STAT 51600 or STAT 51900 . A course in mathematical statistics is desirable, as is a course in regression.

Besides satisfying the general regulations of the Graduate School for the degree of Doctor of Philosophy, the student must complete the following requirements:

Plan of Study

A tentative plan of study should be submitted electronically to the Graduate School by the end of the third session for doctoral students. An individual plan of study is crafted by the student and major professor with the approval of the student's doctoral advisory committee and the department.

Qualifying Examination

There are four Ph.D. qualifying examinations that cover material in methodology, probability, mathematical statistics, and computational statistics and are based on the core courses of the first year of graduate study in statistics.

Preliminary Examination

A student who has submitted an approved plan of study and passed the qualifying exams is required to take a preliminary exam. The purpose of the preliminary exam is to test the preparedness of the student for research. The preliminary exam is an oral exam that is administered by the student’s Ph.D. advisory committee. The student will then be recommended to the Graduate School for admissions to candidacy for the Ph.D degree.

Dissertation

A thesis must be submitted in final form, presenting new results of sufficient importance to merit publication. These results may be theoretical advances in probability or statistics, or methodological advances in the application of probability or statistics. The thesis must be accepted by the advisory committee. The student must present the contents of the thesis in an open examination.

Once a student is admitted to candidacy, the final examination marking completion of the doctoral program must be passed within five calendar years. Extensions of the limit may be granted by the graduate committee on petition by the student and his or her major professor. This may require reapproval of the plan of study and/or retaking of all or part of the Ph.D. degree qualifying examination.

Teaching Experience

Every doctoral candidate is required to teach at least quarter-time for one semester unless decided otherwise by the department.

Upon successful fulfillment of these requirements, the candidate will be recommended to the faculty to receive the Ph.D. degree.

Faculty Research Areas

If you are interested in applying to the Ph.D. Program, please visit How to Apply .

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Statistics PhD theses

2015 onwards.

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A Grand Journey of Statistical Hierarchical Modelling 

Advances in empirical bayes modeling and bayesian computation , advances in statistical network modeling and nonlinear time series modeling , advances in the normal-normal hierarchical model , analysis, modeling, and optimal experimental design under uncertainty: from carbon nano-structures to 3d printing , bayesian biclustering on discrete data: variable selection methods , bayesian learning of relationships , a bayesian perspective on factorial experiments using potential outcomes , building interpretable models: from bayesian networks to neural networks , causal inference under network interference: a framework for experiments on social networks , complications in causal inference: incorporating information observed after treatment is assigned , diagnostic tools in missing data and causal inference on time series , dilemmas in design: from neyman and fisher to 3d printing , distributed and multiphase inference in theory and practice: principles, modeling, and computation for high-throughput science , essays in causal inference and public policy , expediting scientific discoveries with bayesian statistical methods , exploring objective causal inference in case-noncase studies under the rubin causal model , exploring the role of randomization in causal inference , extensions of randomization-based methods for causal inference , g-squared statistic for detecting dependence, additive modeling, and calibration concordance for astrophysical data .

PhD Program information

The Statistics PhD program is rigorous, yet welcoming to students with interdisciplinary interests and different levels of preparation. Students in the PhD program take core courses on the theory and application of probability and statistics during their first year. The second year typically includes additional course work and a transition to research leading to a dissertation. PhD thesis topics are diverse and varied, reflecting the scope of faculty research interests. Many students are involved in interdisciplinary research. Students may also have the option to pursue a designated emphasis (DE) which is an interdisciplinary specialization:  Designated Emphasis in Computational and Genomic Biology ,  Designated Emphasis in Computational Precision Health ,  Designated Emphasis in Computational and Data Science and Engineering . The program requires four semesters of residence.

Normal progress entails:

Year 1 . Perform satisfactorily in preliminary coursework. In the summer, students are required to embark on a short-term research project, internship, graduate student instructorship, reading course, or on another research activity. Years 2-3 . Continue coursework. Find a thesis advisor and an area for the oral qualifying exam. Formally choose a chair for qualifying exam committee, who will also serve as faculty mentor separate from the thesis advisor.  Pass the oral qualifying exam and advance to candidacy by the end of Year 3. Present research at BSTARS each year. Years 4-5 . Finish the thesis and give a lecture based on it in a department seminar.

Program Requirements

• Qualifying Exam

Course work and evaluation

Preliminary stage: the first year.

Effective Fall 2019, students are expected to take four semester-long courses for a letter grade during their first year which should be selected from the core first-year PhD courses offered in the department: Probability (204/205A, 205B,), Theoretical Statistics (210A, 210B), and Applied Statistics (215A, 215B). These requirements can be altered by a member of the PhD Program Committee (in consultation with the faculty mentor and by submitting a graduate student petition ) in the following cases:

• Students primarily focused on probability will be allowed to substitute one semester of the four required semester-long courses with an appropriate course from outside the department.
• Students may request to postpone one semester of the core PhD courses and complete it in the second year, in which case they must take a relevant graduate course in their first year in its place. In all cases, students must complete the first year requirements in their second year as well as maintain the overall expectations of second year coursework, described below. Some examples in which such a request might be approved are described in the course guidance below.
• Students arriving with advanced standing, having completed equivalent coursework at another institution prior to joining the program, may be allowed to take other relevant graduate courses at UC Berkeley to satisfy some or all of the first year requirements

Requirements on course work beyond the first year

Students entering the program before 2022 are required to take five additional graduate courses beyond the four required in the first year, resulting in a total of nine graduate courses required for completion of their PhD. In their second year, students are required to take three graduate courses, at least two of them from the department offerings, and in their third year, they are required to take at least two graduate courses. Students are allowed to change the timing of these five courses with approval of their faculty mentor. Of the nine required graduate courses, students are required to take for credit a total of 24 semester hours of courses offered by the Statistics department numbered 204-272 inclusive. The Head Graduate Advisor (in consultation with the faculty mentor and after submission of a graduate student petition) may consent to substitute courses at a comparable level in other disciplines for some of these departmental graduate courses. In addition, the HGA may waive part of this unit requirement.

Starting with the cohort entering in the 2022-23 academic year , students are required to take at least three additional graduate courses beyond the four required in the first year, resulting in a total of seven graduate courses required for completion of their PhD. Of the seven required graduate courses, five of these courses must be from courses offered by the Statistics department and numbered 204-272, inclusive. With these reduced requirements, there is an expectation of very few waivers from the HGA. We emphasize that these are minimum requirements, and we expect that students will take additional classes of interest, for example on a S/U basis, to further their breadth of knowledge. 

For courses to count toward the coursework requirements students must receive at least a B+ in the course (courses taken S/U do not count, except for STAT 272 which is only offered S/U).  Courses that are research credits, directed study, reading groups, or departmental seminars do not satisfy coursework requirements (for courses offered by the Statistics department the course should be numbered 204-272 to satisfy the requirements). Upper-division undergraduate courses in other departments can be counted toward course requirements with the permission of the Head Graduate Advisor. This will normally only be approved if the courses provide necessary breadth in an application area relevant to the student’s thesis research.

First year course work: For the purposes of satisfactory progression in the first year, grades in the core PhD courses are evaluated as: A+: Excellent performance in PhD program A: Good performance in PhD program A-: Satisfactory performance B+: Performance marginal, needs improvement B: Unsatisfactory performance First year and beyond: At the end of each year, students must meet with his or her faculty mentor to review their progress and assess whether the student is meeting expected milestones. The result of this meeting should be the completion of the student’s annual review form, signed by the mentor ( available here ). If the student has a thesis advisor, the thesis advisor must also sign the annual review form.

Guidance on choosing course work

Choice of courses in the first year: Students enrolling in the fall of 2019 or later are required to take four semesters of the core PhD courses, at least three of which must be taken in their first year. Students have two options for how to schedule their four core courses:

• Option 1 -- Complete Four Core Courses in 1st year: In this option, students would take four core courses in the first year, usually finishing the complete sequence of two of the three sequences.  Students following this option who are primarily interested in statistics would normally take the 210A,B sequence (Theoretical Statistics) and then one of the 205A,B sequence (Probability) or the 215A,B sequence (Applied Statistics), based on their interests, though students are allowed to mix and match, where feasible. Students who opt for taking the full 210AB sequence in the first year should be aware that 210B requires some graduate-level probability concepts that are normally introduced in 205A (or 204).
• Option 2 -- Postponement of one semester of a core course to the second year: In this option, students would take three of the core courses in the first year plus another graduate course, and take the remaining core course in their second year. An example would be a student who wanted to take courses in each of the three sequences. Such a student could take the full year of one sequence and the first semester of another sequence in the first year, and the first semester of the last sequence in the second year (e.g. 210A, 215AB in the first year, and then 204 or 205A in the second year). This would also be a good option for students who would prefer to take 210A and 215A in their first semester but are concerned about their preparation for 210B in the spring semester.  Similarly, a student with strong interests in another discipline, might postpone one of the spring core PhD courses to the second year in order to take a course in that discipline in the first year.  Students who are less mathematically prepared might also be allowed to take the upper division (under-graduate) courses Math 104 and/or 105 in their first year in preparation for 205A and/or 210B in their second year. Students who wish to take this option should consult with their faculty mentor, and then must submit a graduate student petition to the PhD Committee to request permission for  postponement. Such postponement requests will be generally approved for only one course. At all times, students must take four approved graduate courses for a letter grade in their first year.

After the first year: Students with interests primarily in statistics are expected to take at least one semester of each of the core PhD sequences during their studies. Therefore at least one semester (if not both semesters) of the remaining core sequence would normally be completed during the second year. The remaining curriculum for the second and third years would be filled out with further graduate courses in Statistics and with courses from other departments. Students are expected to acquire some experience and proficiency in computing. Students are also expected to attend at least one departmental seminar per week. The precise program of study will be decided in consultation with the student’s faculty mentor.

Remark. Stat 204 is a graduate level probability course that is an alternative to 205AB series that covers probability concepts most commonly found in the applications of probability. It is not taught all years, but does fulfill the requirements of the first year core PhD courses. Students taking Stat 204, who wish to continue in Stat 205B, can do so (after obtaining the approval of the 205B instructor), by taking an intensive one month reading course over winter break.

Designated Emphasis: Students with a Designated Emphasis in Computational and Genomic Biology or Designated Emphasis in Computational and Data Science and Engineering should, like other statistics students, acquire a firm foundation in statistics and probability, with a program of study similar to those above. These programs have additional requirements as well. Interested students should consult with the graduate advisor of these programs. 

Starting in the Fall of 2019, PhD students are required in their first year to take four semesters of the core PhD courses. Students intending to specialize in Probability, however, have the option to substitute an advanced mathematics class for one of these four courses. Such students will thus be required to take Stat 205A/B in the first year,  at least one of Stat 210A/B or Stat 215A/B in the first year, in addition to an advanced mathematics course. This substitute course will be selected in consultation with their faculty mentor, with some possible courses suggested below. Students arriving with advanced coursework equivalent to that of 205AB can obtain permission to substitute in other advanced probability and mathematics coursework during their first year, and should consult with the PhD committee for such a waiver.

During their second and third years, students with a probability focus are expected to take advanced probability courses (e.g., Stat 206 and Stat 260) to fulfill the coursework requirements that follow the first year. Students are also expected to attend at least one departmental seminar per week, usually the probability seminar. If they are not sufficiently familiar with measure theory and functional analysis, then they should take one or both of Math 202A and Math 202B. Other recommended courses from the department of Mathematics or EECS include:

Math 204, 222 (ODE, PDE) Math 205 (Complex Analysis) Math 258 (Classical harmonic analysis) EE 229 (Information Theory and Coding) CS 271 (Randomness and computation)

The Qualifying Examination 

The oral qualifying examination is meant to determine whether the student is ready to enter the research phase of graduate studies. It consists of a 50-minute lecture by the student on a topic selected jointly by the student and the thesis advisor. The examination committee consists of at least four faculty members to be approved by the department.  At least two members of the committee must consist of faculty from the Statistics and must be members of the Academic Senate. The chair must be a member of the student’s degree-granting program.

Qualifying Exam Chair. For qualifying exam committees formed in the Fall of 2019 or later, the qualifying exam chair will also serve as the student’s departmental mentor, unless a student already has two thesis advisors. The student must select a qualifying exam chair and obtain their agreement to serve as their qualifying exam chair and faculty mentor. The student's prospective thesis advisor cannot chair the examination committee. Selection of the chair can be done well in advance of the qualifying exam and the rest of the qualifying committee, and because the qualifying exam chair also serves as the student’s departmental mentor (unless the student has co-advisors), the chair is expected to be selected by the beginning of the third year or at the beginning of the semester of the qualifying exam, whichever comes earlier. For more details regarding the selection of the Qualifying Exam Chair, see the "Mentoring" tab.  

Paperwork and Application. Students at the point of taking a qualifying exam are assumed to have already found a thesis advisor and to should have already submitted the internal departmental form to the Graduate Student Services Advisor ( found here ).  Selection of a qualifying exam chair requires that the faculty member formally agree by signing the internal department form ( found here ) and the student must submit this form to the Graduate Student Services Advisor.  In order to apply to take the exam, the student must submit the Application for the Qualifying Exam via CalCentral at least three weeks prior to the exam. If the student passes the exam, they can then officially advance to candidacy for the Ph.D. If the student fails the exam, the committee may vote to allow a second attempt. Regulations of the Graduate Division permit at most two attempts to pass the oral qualifying exam. After passing the exam, the student must submit the Application for Candidacy via CalCentral .

The Doctoral Thesis

The Ph.D. degree is granted upon completion of an original thesis acceptable to a committee of at least three faculty members. The majority or at least half of the committee must consist of faculty from Statistics and must be members of the Academic Senate. The thesis should be presented at an appropriate seminar in the department prior to filing with the Dean of the Graduate Division. See Alumni if you would like to view thesis titles of former PhD Students.

Graduate Division offers various resources, including a workshop, on how to write a thesis, from beginning to end. Requirements for the format of the thesis are rather strict. For workshop dates and guidelines for submitting a dissertation, visit the Graduate Division website.

Students who have advanced from candidacy (i.e. have taken their qualifying exam and submitted the advancement to candidacy application) must have a joint meeting with their QE chair and their PhD advisor to discuss their thesis progression; if students are co-advised, this should be a joint meeting with their co-advisors. This annual review is required by Graduate Division.  For more information regarding this requirement, please see  https://grad.berkeley.edu/ policy/degrees-policy/#f35- annual-review-of-doctoral- candidates .

Teaching Requirement

For students enrolled in the graduate program before Fall 2016, students are required to serve as a Graduate Student Instructor (GSI) for a minimum of 20 hours (equivalent to a 50% GSI appointment) during a regular academic semester by the end of their third year in the program.

Effective with the Fall 2016 entering class, students are required to serve as a GSI for a minimum of two 50% GSI appointment during the regular academic semesters prior to graduation (20 hours a week is equivalent to a 50% GSI appointment for a semester) for Statistics courses numbered 150 and above. Exceptions to this policy are routinely made by the department.

Each spring, the department hosts an annual conference called BSTARS . Both students and industry alliance partners present research in the form of posters and lightning talks. All students in their second year and beyond are required to present a poster at BSTARS each year. This requirement is intended to acclimate students to presenting their research and allow the department generally to see the fruits of their research. It is also an opportunity for less advanced students to see examples of research of more senior students. However, any students who do not yet have research to present can be exempted at the request of their thesis advisor (or their faculty mentors if an advisor has not yet been determined).

Mentoring for PhD Students

Initial Mentoring: PhD students will be assigned a faculty mentor in the summer before their first year. This faculty mentor at this stage is not expected to be the student’s PhD advisor nor even have research interests that closely align with the student. The job of this faculty mentor is primarily to advise the student on how to find a thesis advisor and in selecting appropriate courses, as well as other degree-related topics such as applying for fellowships.  Students should meet with their faculty mentors twice a semester. This faculty member will be the designated faculty mentor for the student during roughly their first two years, at which point students will find a qualifying exam chair who will take over the role of mentoring the student.

Research-focused mentoring : Once students have found a thesis advisor, that person will naturally be the faculty member most directly overseeing the student’s progression. However, students will also choose an additional faculty member to serve as a the chair of their qualifying exam and who will also serve as a faculty mentor for the student and as a member of his/her thesis committee. (For students who have two thesis advisors, however, there is not an additional faculty mentor, and the quals chair does NOT serve as the faculty mentor).

The student will be responsible for identifying and asking a faculty member to be the chair of his/her quals committee. Students should determine their qualifying exam chair either at the beginning of the semester of the qualifying exam or in the fall semester of the third year, whichever is earlier. Students are expected to have narrowed in on a thesis advisor and research topic by the fall semester of their third year (and may have already taken qualifying exams), but in the case where this has not happened, such students should find a quals chair as soon as feasible afterward to serve as faculty mentor.

Students are required to meet with their QE chair once a semester during the academic year. In the fall, this meeting will generally be just a meeting with the student and the QE chair, but in the spring it must be a joint meeting with the student, the QE chair, and the PhD advisor. If students are co-advised, this should be a joint meeting with their co-advisors.

If there is a need for a substitute faculty mentor (e.g. existing faculty mentor is on sabbatical or there has been a significant shift in research direction), the student should bring this to the attention of the PhD Committee for assistance.

PhD Student Forms:

Important milestones: .

Each of these milestones is not complete until you have filled out the requisite form and submitted it to the GSAO. If you are not meeting these milestones by the below deadline, you need to meet with the Head Graduate Advisor to ask for an extension. Otherwise, you will be in danger of not being in good academic standing and being ineligible for continued funding (including GSI or GSR appointments, and many fellowships). 

†Students who are considering a co-advisor, should have at least one advisor formally identified by the end of the second year; the co-advisor should be identified by the end of the fall semester of the 3rd year in lieu of finding a Research Mentor/QE Chair.

Expected Progress Reviews: 

* These meetings do not need to be held in the semester that you take your Qualifying Exam, since the relevant people should be members of your exam committee and will discuss your research progress during your qualifying exam

** If you are being co-advised by someone who is not your primary advisor because your primary advisor cannot be your sole advisor, you should be meeting with that person like a research mentor, if not more frequently, to keep them apprised of your progress. However, if both of your co-advisors are leading your research (perhaps independently) and meeting with you frequently throughout the semester, you do not need to give a fall research progress report.

Recent PhD Theses

Additional theses can be found on UWSpace . 

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Digital Commons @ USF > USF Health > College of Public Health > Epidemiology and Biostatistics > Theses and Dissertations

Epidemiology and Biostatistics Theses and Dissertations

Theses/dissertations from 2023 2023.

Gender Differences in Episodic Memory in Later Life: The Mediating Role of Education , Sara Robinson

Theses/Dissertations from 2022 2022

Nonparametric Estimation of Transition Probabilities in Illness-Death Model based on Ranked Set Sampling , Ying Ma

Theses/Dissertations from 2021 2021

Bayesian Multivariate Joint Modeling for Skewed-longitudinal and Time-to-event Data , Lan Xu

Theses/Dissertations from 2020 2020

Identifying Barriers and Facilitators to Improve Hepatitis C Virus Screening , Linh M. Duong

Quantifying the Impact of Chronic Stress on Racial Disparities in Cardiovascular Disease , Nnadozie Emechebe

A Review of American College Campus Tobacco or Smoke free Policies: A Case Study of a Large Urban University , Sarah E. Powell

Theses/Dissertations from 2019 2019

Evolutionary Dynamics of Influenza Type B in the Presence of Vaccination: An Ecological Study , Lindsey J. Fiedler

Respiratory Infections and Risk for Development of Narcolepsy: Analysis of the Truven Health MarketScan Database (2008 to 2010) with Additional Assessment of Incidence and Prevalence , Darren Scheer

Multimodal Treatment and Neoadjuvant Chemotherapy Trends, Utilization and Survival Effects in Intrahepatic Cholangiocarcinoma – a Propensity Score Analysis , Ovie Utuama

Theses/Dissertations from 2018 2018

Flowgraph Models for Clustered Multistate Time to Event Data , Kristin Hall

Impact of Obesity and Expression of Obesity-Related Genes in the Progression of Prostate Cancer in African American Men , Mmadili Nancy Ilozumba

Angiostrongylus cantonensis: Epidemiologic Review, Location-Specific Habitat Modelling, and Surveillance in Hillsborough County, Florida, U.S.A. , Brad Christian Perich

Strategies to Adjust for Response Bias in Clinical Trials: A Simulation Study , Victoria R. Swaidan

Theses/Dissertations from 2017 2017

Sleep and Alzheimer’s disease: A critical examination of the risk that Sleep Problems or Disorders particularly Obstructive Sleep Apnea pose towards developing Alzheimer’s disease , Omonigho A. Michael Bubu

Deployment, Post-Traumatic Stress Disorder and Hypertensive Disorders of Pregnancy among U.S. Active-Duty Military Women , Michelle C. Nash

Ambient Ozone and Cadmium as Risk Factors For Congenital Diaphragmatic Hernia , Rema Ramakrishnan

Ambient Benzene and PM2.5 Exposure during Pregnancy: Examining the Impact of Exposure Assessment Decisions on Associations between Birth Defects and Air Pollution , Jean Paul Tanner

Bayesian inference on quantile regression-based mixed-effects joint models for longitudinal-survival data from AIDS studies , Hanze Zhang

Theses/Dissertations from 2016 2016

Sleep Duration Patterns from Adolescence to Young Adulthood and their Impact on Asthma and Inflammation , Chighaf Bakour

Efficiency of an Unbalanced Design in Collecting Time to Event Data with Interval Censoring , Peiyao Cheng

Association between Folate Levels and Preterm Birth in Tampa, Florida , Carolyn Heeraman

HIV/STIs and Intimate Partner Violence: Results from the Togo 2013-2014 Demographic and Health Surveys , Anthony H. Nguyen

Incidence, Persistence, and Recurrence of Anogenital α- Mucosal HPV Infections (HPV 6, 11, 16, 18, 31, 33, 45, 52 and 58) , Shitaldas J. Pamnani

Factors Associated with Sexually Transmitted Infections (STIs) and Multiple STI Co-infections: Results from the EVRI HIV Prevention Preparedness Trial , Ubin Pokharel

Hidden Markov Chain Analysis: Impact of Misclassification on Effect of Covariates in Disease Progression and Regression , Haritha Polisetti

Association of Known and Unknown Oncoviruses with External Genital Lesion (EGL) Manifestations in a Multinational Cohort of Men , Shams Ur Rahman

Racial and Ethnic Differences in Low-Risk Cesarean Deliveries in Florida , Yuri Combo Vanda Sebastiao

The Effects of Personal and Family History of Cancer on the Development of Dementia in Japanese Americans: The KAME Project , Adam Lee Slotnick

Rhabdomyosarcoma Incidence and Survival in Whites, Blacks, and Hispanics from 1973-2013: Analysis from the Surveillance, Epidemiology, and End Results Program , Heather Tinsley

Theses/Dissertations from 2015 2015

Assessment of the impact of Attention Deficit Hyperactivity Disorder on Type 1 Diabetes , Kellee Miller

Bayesian Inference on Longitudinal Semi-continuous Substance Abuse/Dependence Symptoms Data , Dongyuan Xing

Theses/Dissertations from 2014 2014

Statistical Analysis and Modeling of PM 2.5 Speciation Metals and Their Mixtures , Boubakari Ibrahimou

Elective Early Term Delivery and Adverse Infant Outcomes in a Population-Based Multiethnic Cohort , Jason Lee Salemi

Theses/Dissertations from 2013 2013

Uncontrolled Hypertension and Associated Factors in Hypertensive Patients at the Primary Healthcare Center Luis H. Moreno, Panama: A Feasibility Study , Roderick Ramon Chen Camano

An Analysis of the Association between Animal Exposures and the Development of Type 1 Diabetes in the TEDDY Cohort , Callyn Hall

Multiple Calibrations in Integrative Data Analysis: A Simulation Study and Application to Multidimensional Family Therapy , Kristin Wynn Hall

Mother- to - Child Transmission of HIV and congenital syphilis: A snapshot of an Epidemic in the Republic of Panama , Lorna Elizabeth Jenkins

A Latent Mixture Approach to Modeling Zero-Inflated Bivariate Ordinal Data , Rajendra Kadel

Associations of Perceived Stress, Sleep, and Human Papillomavirus in a Prospective Cohort of Men , Stephanie Kay Kolar

Influence of Maternal Thyroid Dysfunction on Infant Growth and Development , Ronee Elisha Wilson

Theses/Dissertations from 2012 2012

Bayesian Inference on Mixed-effects Models with Skewed Distributions for HIV longitudinal Data , Ren Chen

Linear Mixed-Effects Models: Applications to the Behavioral Sciences and Adolescent Community Health , Lizmarie Gabriela Maldonado

Statistical Estimation of Physiologically-based Pharmacokinetic Models: Identifiability, Variation, and Uncertainty with an Illustration of Chronic Exposure to Dioxin and Dioxin-like-compounds. , Zachary John Thompson

Evaluation of Repeated Biomarkers: Non-parametric Comparison of Areas under the Receiver Operating Curve Between Correlated Groups Using an Optimal Weighting Scheme , Ping Xu

Theses/Dissertations from 2011 2011

The Natural History of Human Papillomavirus Related Condyloma In a Multinational Cohort of Men , Gabriella Anic

Characterization of the Serologic Responses to Plasmodium vivax DBPII Variants Among Inhabitants of Pursat Province, Cambodia , Samantha Jones Barnes

Disparities in Survival and Mortality among Infants with Congenital Aortic, Pulmonary, and Tricuspid Valve Defects by Maternal Race/Ethnicity and Infant Sex , Colleen Conklin

Case-Control Study of Sunlight Exposure and Cutaneous Human Papillomavirus Seroreactivity in Basal Cell and Squamous Cell Carcinomas of the Skin , Michelle R. Iannacone

Assessing the Relationship of Monocytes with Primary and Secondary Dengue Infection among Hospitalized Dengue Patients in Malaysia, 2010: A Cross-Sectional Study , Benjamin Glenn Klekamp

Gender Differences in Lung Cancer Treatment and Survival , Margaret Anne Kowski

An examination of diet, acculturation and risk factors for heart disease among Jamaican immigrants , Carol Renee Oladele

Indicators of Early Adult and Current Personality in Parkinson's Disease , Kelly Sullivan

Theses/Dissertations from 2010 2010

Does Patient Dementia Limit the Use of Cardiac Catheterization in ST-Elevated Myocardial Infarction? , Marianne Chanti-Ketterl

Extending the Principal Stratification Method To Multi-Level Randomized Trials , Jing Guo

Serum Antibodies to Human Papillomavirus Type 6, 11, 16 and 18 and Their Role in the Natural History of HPV Infection in Men , Beibei Lu

Evaluation of Common Inherited Variants in Mitochondrial-Related and MicroRNA-Related Genes as Novel Risk Factors for Ovarian Cancer , Jennifer Permuth Wey

DNA Methylation and its Association with Prenatal Exposures and Pregnancy Outcomes , Jennifer Straughen

Theses/Dissertations from 2009 2009

Cardiovascular risk factors for mild cognitive impairment , Michael Malek-Ahmadi

Additive Latent Variable (ALV) Modeling: Assessing Variation in Intervention Impact in Randomized Field Trials , Peter Ayo Toyinbo

Theses/Dissertations from 2008 2008

A Comparison of Community-Based Centers versus University-Based Centers in Clinical Trial Performance , Cynthia R. Stockddale

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Statistics and Actuarial Science

Graduate theses.

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Below is a list of the theses produced by graduate students in the Department of Statistics and Actuarial Science.

Projects and Theses From Previous Years

2015 - 2019 2010 - 2014 2005 - 2009 2000 - 2004 1990's 1980's and prior

How to write a PhD thesis: a step-by-step guide

A draft isn’t a perfect, finished product; it is your opportunity to start getting words down on paper, writes Kelly Louise Preece

Kelly Louise Preece

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Congratulations; you’ve finished your research! Time to write your PhD thesis. This resource will take you through an eight-step plan for drafting your chapters and your thesis as a whole. 

Organise your material

Before you start, it’s important to get organised. Take a step back and look at the data you have, then reorganise your research. Which parts of it are central to your thesis and which bits need putting to one side? Label and organise everything using logical folders – make it easy for yourself! Academic and blogger Pat Thomson calls this  “Clean up to get clearer” . Thomson suggests these questions to ask yourself before you start writing:

• What data do you have? You might find it useful to write out a list of types of data (your supervisor will find this list useful too.) This list is also an audit document that can go in your thesis. Do you have any for the “cutting room floor”? Take a deep breath and put it in a separate non-thesis file. You can easily retrieve it if it turns out you need it.
• What do you have already written? What chunks of material have you written so far that could form the basis of pieces of the thesis text? They will most likely need to be revised but they are useful starting points. Do you have any holding text? That is material you already know has to be rewritten but contains information that will be the basis of a new piece of text.
• What have you read and what do you still need to read? Are there new texts that you need to consult now after your analysis? What readings can you now put to one side, knowing that they aren’t useful for this thesis – although they might be useful at another time?
• What goes with what? Can you create chunks or themes of materials that are going to form the basis of some chunks of your text, perhaps even chapters?

Once you have assessed and sorted what you have collected and generated you will be in much better shape to approach the big task of composing the dissertation. 

Decide on a key message

A key message is a summary of new information communicated in your thesis. You should have started to map this out already in the section on argument and contribution – an overarching argument with building blocks that you will flesh out in individual chapters.

You have already mapped your argument visually, now you need to begin writing it in prose. Following another of Pat Thomson’s exercises, write a “tiny text” thesis abstract. This doesn’t have to be elegant, or indeed the finished product, but it will help you articulate the argument you want your thesis to make. You create a tiny text using a five-paragraph structure:

• The first sentence addresses the broad context. This locates the study in a policy, practice or research field.
• The second sentence establishes a problem related to the broad context you have set out. It often starts with “But”, “Yet” or “However”.
• The third sentence says what specific research has been done. This often starts with “This research” or “I report…”
• The fourth sentence reports the results. Don’t try to be too tricky here, just start with something like: “This study shows,” or “Analysis of the data suggests that…”
• The fifth and final sentence addresses the “So What?” question and makes clear the claim to contribution.

Here’s an example that Thomson provides:

Secondary school arts are in trouble, as the fall in enrolments in arts subjects dramatically attests. However, there is patchy evidence about the benefits of studying arts subjects at school and this makes it hard to argue why the drop in arts enrolments matters. This thesis reports on research which attempts to provide some answers to this problem – a longitudinal study which followed two groups of senior secondary students, one group enrolled in arts subjects and the other not, for three years. The results of the study demonstrate the benefits of young people’s engagement in arts activities, both in and out of school, as well as the connections between the two. The study not only adds to what is known about the benefits of both formal and informal arts education but also provides robust evidence for policymakers and practitioners arguing for the benefits of the arts. You can  find out more about tiny texts and thesis abstracts on Thomson’s blog.

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Write a plan

You might not be a planner when it comes to writing. You might prefer to sit, type and think through ideas as you go. That’s OK. Everybody works differently. But one of the benefits of planning your writing is that your plan can help you when you get stuck. It can help with writer’s block (more on this shortly!) but also maintain clarity of intention and purpose in your writing.

You can do this by creating a  thesis skeleton or storyboard , planning the order of your chapters, thinking of potential titles (which may change at a later stage), noting down what each chapter/section will cover and considering how many words you will dedicate to each chapter (make sure the total doesn’t exceed the maximum word limit allowed).

Use your plan to help prompt your writing when you get stuck and to develop clarity in your writing.

Some starting points include:

• This chapter will argue that…
• This section illustrates that…
• This paragraph provides evidence that…

Of course, we wish it werethat easy. But you need to approach your first draft as exactly that: a draft. It isn’t a perfect, finished product; it is your opportunity to start getting words down on paper. Start with whichever chapter you feel you want to write first; you don’t necessarily have to write the introduction first. Depending on your research, you may find it easier to begin with your empirical/data chapters.

Vitae advocates for the “three draft approach” to help with this and to stop you from focusing on finding exactly the right word or transition as part of your first draft.

This resource originally appeared on Researcher Development .

Kelly Louse Preece is head of educator development at the University of Exeter.

If you would like advice and insight from academics and university staff delivered direct to your inbox each week, sign up for the Campus newsletter .

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Home > STUDENT_SCHOLAR > ENG_PHD_THESES > 51

Engineering Ph.D. Theses

Cnn feature map interpretation and key-point detection using statistics of activation layers, date of award, document type.

Dissertation

Santa Clara : Santa Clara University, 2023.

Degree Name

Doctor of Philosophy (PhD)

Electrical and Computer Engineering

First Advisor

Convolutional Neural Networks (CNNs) have evolved to be very accurate for the classification of image objects from a single image or frames in video. A major function in a CNN model is the extraction and encoding of features from training or ground truth images, and simple CNN models are trained to identify a dominant object in an image from the feature encodings. More complex models such as RCNN and others can identify and locate multiple objects in an image. Feature Maps from trained CNNs contain useful information beyond the encoding for classification or detection. By examining the maximum activation values and statistics from early layer feature maps it is possible to identify key points of objects, including location, particularly object types that were included in the original training data set. Methods are introduced that leverage the key points extracted from these early layers to isolate objects for more accurate classification and detection, using simpler networks compared to more complex, integrated networks.

An examination of the feature extraction process will provide insight into the information that is available in the various feature map layers of a CNN. While a basic CNN model does not explicitly create instances of visual or other types of information expression, it is possible to examine the Feature Map layers and create a framework for interpreting these layers. This can be valuable in a variety of different goals such object location and size, feature statistics, and redundancy analysis. In this thesis we examine in detail the interpretation of Feature Maps in CNN models, and develop a method for extracting information from trained convolutional layers to locate objects belonging to a pre-trained image data set. A major contribution of this work is the analysis of statistical characteristics of early layer feature maps and development of a method of identifying key-points of objects without the benefit of information from deeper layers. A second contribution is analysis of the accuracy of the selections as key-points of objects present in the image. A third contribution is the clustering of key-points to form partitions for cropping the original image and computing detection using the simple CNN model.

This key-point detection method has the potential to greatly improve the classification capability of simple CNNs by making it possible to identify multiple objects in a complex input image, with a modest computation cost, and also provide localization information.

Recommended Citation

Rush, Allen, "CNN Feature Map Interpretation and Key-Point Detection Using Statistics of Activation Layers" (2023). Engineering Ph.D. Theses . 51. https://scholarcommons.scu.edu/eng_phd_theses/51

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2024 Department Dissertation Awards

With sincere appreciation for all those involved in the nomination and review process, the Department of Statistics proudly announces the winners of the full group of doctoral dissertation awards this year. Each hard-won distinction is accompanied by a prize of $1,000, and recipients will be presented with their certificates during the department's diploma ceremony on June 16th. Congratulations to these outstanding students!

Theodore W. Anderson Theory of Statistics Dissertation Award

Isaac Gibbs – for his groundbreaking work on adaptive conformal inference, maintaining prediction coverage over time despite substantial changes in the data distribution, and his amazing contribution to conformal prediction, quantifying the uncertainty of modern black box algorithms without distributional assumptions.

Jerome H. Friedman Applied Statistics Dissertation Award

Sifan Liu – for her work on high dimensional integration, machine learning optimization strategies and pre-integration in randomized quasi-Monte Carlo, and its novel application in data science.

Ingram Olkin Interdisciplinary Research Dissertation Award

Ying Jin – for pioneering model-free selective inference methods for multi-stage decision pipelines such as job hiring and drug discovery, and for providing new methods for diagnosing replication failure.

Probability Dissertation Award

Kangjie Zhou – for discovering precise high-dimensional asymptotics for projection pursuit with random data, using techniques from spin glasses and empirical process theory.

Laura V. Machia, Ph.D. 430 Huntington Hall [email protected] (315)443-2354

Sara E. Burke, Ph.D., Jennifer Clarke, Ph.D., Brett K. Jakubiak, Ph.D., Jessie Joyce, Ph.D., Laura V. Machia, Ph.D., Leonard S. Newman, Ph.D., Jeewon Oh, Ph.D., and Zahra Vahedi, Ph.D.

Program Description:

Since its creation in 1924, the program has embraced research as a central focus for the training of social psychologists. We train students with the skills necessary to function as applied or research scientists within one or more of the many sub-domains of social psychology. Our program explicitly adopts multidisciplinary themes to create a unique graduate training experience. The central focus of the social psychology program is the scholarship of the causes, consequences, and/or remediation of social challenges. Students are encouraged to pursue specific research interests that complement this broad programmatic theme.

Student Learning Outcomes

1) Demonstrate broad knowledge of the field of social psychology and a deep understanding of its basic principles - Examine the causes, consequences, and/or remediation of social challenges

2) Conduct reviews of the social psychology literature and integrate/synthesize that literature

3) Design and conduct systematic research of important challenges facing society

4) Utilize classic and contemporary quantitative methods to conduct statistical analysis for their research

5) Present research by means of poster presentations and/or talks at professional conferences

6) Follow ethical guidelines of the American Psychological Association

7) Demonstrate expertise as a psychology instructor

Program Requirements

Consistent with the general goal of the program, students are strongly encouraged to become involved in research at an early point in their training by participating in faculty research projects and by carrying out individual research under the guidance of faculty members. Accordingly, all students obtain extensive training in research methods, both within a classroom setting and in actual research practice. Students are required to take 90 credits of coursework and complete a series of Milestones.

Required Coursework

The courses offered in the program consist of intensive exposure to the prominent theories and methods in social psychology. 

Conceptual Core (15 credit hours)

• PSY 674 - Advanced Social Psychology 3 credit(s)
• PSY 677 - Social Cognition 3 credit(s)
• PSY 693 - Advanced Personality 3 credit(s)
• PSY 775 - Seminar in Social Psychology 3 credit(s) (This must be taken at least twice)

Department Core (9 credit hours)

An additional 9 credit hours of PSY courses outside of social psychology. These courses should be selected in consultation with the advisor to optimize the student’s training.

Statistics Core (6 credit hours)

• PSY 655 - Experimental Design and Statistical Methods I 3 credit(s)
• PSY 756 - Experimental Design and Statistical Methods II 3 credit(s)

Methods Core (minimum of 9 credit hours)

• PSY 624 - Graduate Seminar in Psychological Methods 3 credit(s)
• PSY 627 - Proseminar Methods and Topics in Social Psychology 3 credit(s)

(This must be taken at least twice)

Dissertation (18 credits)

• PSY 999 - Dissertation 1-15 credit(s)

Independent Research or Other Courses

Students chose additional courses to complete the minimum 90 credits for the PhD. Students are encouraged to work closely with one or more faculty members in a research program and to develop a program of research. Research is reflected in courses including PSY 997, 690, or 990. Students should take courses that strengthen their training. Electives should be selected in consultation with the advisor. We strongly recommend students select electives that will further their statistical or methodological skills.

Total Credits Required (90 credits)

In addition to the required coursework, all students must complete the following milestones:

• Give a research presentation at Brownbag during the first year.
• All students are required to complete a Masters. Students who completed a Master’s thesis elsewhere may petition for that thesis to satisfy this requirement.
• Successfully pass a Qualifying Examination.
• Successfully complete a dissertation

Optional Concentrations

Please keep the “triple dipping rule” in mind as you consider the following optional programs to complement your MA and PhD programs.

The triple dipping rule - Per university policy (link: http://coursecatalog.syr.edu/content.php?catoid=25&navoid=3251#34-0), specific courses/credits can be counted toward up to two (but no more than two) graduate programs or degree. The courses listed in the Program of Study for the Master’s in Psychology count towards the PhD in Social Psychology.

Concentration in Neuroscience (optional)

Requirements.

Complete the following courses:

• BIO 607 - Advanced Neuroscience 3 credit(s)
• NEU 614 - Interdisciplinary Methods of Neuroscience 0-3 credit(s)
• NEU 613 - Readings in Neuroscience 0-3 credit(s)
• PSY 777 - Advanced Cognitive Neuroscience 3 credit(s)

In addition, students are expected to:

Present at least one special seminar and participate in other research days organized or sponsored by the Interdisciplinary Neuroscience Program during your tenure as a student.

Attend program-sponsored seminars given by outside speakers, graduate students, postdocs, and faculty.

Concentration in Advanced Quantitative Methods in Psychology (optional)

The program has two goals. First, students will receive training in a wide range of advanced statistics or quantitative methods. Such breadth assures that students have maximum flexibility in designing a curriculum that best fits their individual career goals. Second, the program emphasizes competence in the application of knowledge and analytic skills acquired through coursework to students’ own research.  Together these will help promote the pursuit of high-quality research and research-focused careers in academic and non-academic settings.

Pre-requisites

Requirements (part a).

12 credit hours of coursework focusing on statistical or quantitative methods at the 500-level or above. Select from these courses:

• CSE 581 - Introduction to Database Management Systems 3 credit(s)
• IST 718 - Big Data Analytics 3 credit(s)
• MAT 521 - Introduction to Probability 3 credit(s)
• MAT 525 - Mathematical Statistics 3 credit(s)
• MAT 651 - Probability and Statistics I 3 credit(s)
• MAT 652 - Probability and Statistics II 3 credit(s)
• MAT 750 - Statistical Consulting 3 credit(s)
• PSY 612 - Advanced Experimental Psychology 3 credit(s)
• PSY 653 - Psychological Measurement 3 credit(s)
• PSY 780 - Introduction to Structural Equation Modeling 3 credit(s)
• PSY 854 - Bayesian Statistical Analysis 3 credit(s)

To demonstrate the minimum level of competence, students must earn a B- or better in each of the courses.

Courses may count toward the certificate and other degrees so long as the ‘triple dipping’ rule and any other university policies are met.

Requirements (part b)

An approved empirical research product demonstrating competence in the use of an advanced statistical or quantitative method.

A research product that demonstrates competence in the use of an advanced statistical or quantitative method may include one of the following options:

(b-1) submitting a manuscript based on empirical research using an advanced statistical or quantitative method for peer review, or

(b-2) successfully defending a thesis, qualifying exam, or dissertation using an advanced statistical or quantitative method. Specific statistical or quantitative methods on which the product is based may be different from those in the student’s elective coursework or desired specialization areas in psychology.

To confirm that this requirement is met, the student must

• submit to the committee a two-paragraph description about at the initiation of the project or proposal of the milestone: indicate the advanced statistical or quantitative method to be used in their project, along with a statement that the student alone will conduct the advanced statistical or quantitative method analysis. The committee will indicate if the proposal is sufficient for this requirement.
• After the completion of the project, the committee must review and approve the final product along with a short statement confirming that they conducted the advanced statistical or quantitative method.

The program is strongly committed to the recruitment of individuals from diverse backgrounds.  Applications are considered for the fall term only, and the deadline for receipt of the completed application is December 1. Only full-time students are considered for admission. 

The admissions committee consists of social psychology area faculty members. This committee makes decisions on the admission of applicants to graduate school; students who have or will soon complete either bachelor’s or master’s degrees, and who qualify in the judgment of this committee are admitted. To make this judgment, the committee considers a candidate’s complete application and whether the research interests of this student matches with a member of the faculty.

Financial Support

The department makes a determined effort to offer each student who is in good standing financial support in the form of a stipend and tuition remission. Stipends may stem from several sources including, teaching assistantships, research assistantships, and fellowships. Outstanding students are placed into competition for University-wide fellowships. In addition, students are encouraged to apply for available external funding.

Satisfactory Progress

Students’ progress is reviewed by the program faculty each year. The requirements for satisfactory progress are as follows:

(a) Academic or course-related requirements. Students should make progress toward completing their coursework.  A cumulative GPA of 3.0 or better, exclusive of independent study courses, is required to maintain good standing with regard to GPA. In addition, students are required to earn a grade of B or better in all required courses.

(b) Research

Students are expected to actively participate in a research group, demonstrate the ability to function independently in all phases of the research process, and make timely progress toward completion of research requirements.

Deadlines for Research milestones (note that these are deadlines, but we recommend earlier completion of defenses):

• a research presentation at Brownbag by May 30 of the first year
• successfully defending the master’s thesis by May 15 of the third year
• submitting a first attempt at passing the qualifying examination by August 15 of the third year (successfully passing the qualifying examination by August 15 of the fourth year)
• successfully defending the doctoral dissertation in time to submit by the Graduate School deadline for an August graduation of fifth year.

c) Professional Development

Students are expected to develop professional skills and materials in preparation for a scientific career, broadly speaking. 

In addition, all students who receive department funding as a Teaching Assistant will be evaluated each semester by the faculty member assigned to the course. Each student’s overall performance will be assessed (e.g., teaching effort and performance, attendance, meeting deadlines, following course guidelines and policies, professionalism, etc.). In addition, if the TA assignment includes teaching, the faculty member may conduct an in-class observation to evaluate each student’s teaching skills and individualized feedback will be provided. It is expected that a student’s overall performance each semester, as assessed by the faculty member assigned to the course, will meet or exceed expectations in order for a student to remain in good standing in the program. 

The Doctoral Degrees (Ph.D. in Mathematics and Ph.D. in Statistics) in the Department of Mathematics and Statistics are research degrees. Students in the Ph.D. program are to maintain a balance between the depth of the dissertation work and the breadth provided by the course work. The programs prepare students for academic careers balancing teaching and research, or, especially in the case of the statistics Ph.D., research-oriented jobs in government and industry.  

Learning Outcomes

Upon completion of the PhD degree, students in the Statistics program are expected to be able to:

• Effectively explain, integrate, and apply critical concepts in statistics
• Clearly communicate statistical ideas orally and in writing
• Use appropriate technology to successfully make progress on a wide variety of statistical tasks
• Read, understand, critique, and extend published articles
• Conduct original research in mathematics and write a dissertation of publishable quality

Admission Requirements

Deadlines:  Summer and Fall, Jan 31 recommended for funding. Applicants to the PhD programs in Mathematics and in Statistics are required to have a Master’s degree by the time they start classes at BGSU. If you are currently in a master’s program, please indicate clearly when you expect to finish that degree program in your application under the Academic History tab. When evaluating applications, we examine the student’s ability to start immediately in PhD-level courses offered the next Fall, because the first requirement for PhD students is to take two PhD-level sequences and pass qualifying examinations. This assists in preserving time to conduct dissertation research and finish the degree in a 4-year time frame. In the event that assistantship funding is available, the department can offer two years of support for the Master’s program and four years of support for the PhD program. Additional documents required:

• Three Letters of Recommendation from faculty or professionals who can assess your academic preparation for the program
• Statement of Purpose

International applicants are required to submit scores from the Test of English as a Foreign Language (TOEFL), the International English Language Testing System (IELTS), or the Pearson Test of English Academic (PTEA). Successful completion of ELS 112 will also be accepted for this requirement.  Additionally, Duolingo test scores will be accepted for applications through Summer 2025. Applicants of the Graduate College who have completed a previous degree (associate, bachelor’s master’s or doctorate) from a U.S. college/university or are from a country (click  here  for a complete list) in which instruction was delivered in English (and attended the university for at least two years) are exempt from providing these test scores.

Application Requirements

Admissions Categories and Grade Point Average Requirements

International Application Information

Degree Requirements

Curriculum requirements, required courses (24 credits).

Student must earn a gade of “B” or better in all required courses except MATH 6650. 

• MATH 6570 - Statistical Computing
• MATH 6650 - Real Analysis I
• MATH 7410 - Advanced Probability Theory I
• MATH 7450 - Advanced Mathematical Statistics
• MATH 7460 - Advanced Mathematical Statistics
• MATH 7550 - Statistical Learning I
• MATH 7560 - Statistical Learning II
• MATH 7570 - Linear Statistical Inference

Electives (18-20 credits)

Select 5 courses from:

• MATH 6440 - Stochastic Processes
• MATH 6450 - Statistical Distribution Theory
• MATH 6460 - Nonparametric Statistical Inference
• MATH 6470 - Sequential Statistical Inference
• MATH 6480 - Bayesian Statistical Inference
• MATH 6490 - Statistical Graphics
• MATH 6710 - Survival Analysis
• MATH 6720 - Biostatistical Methods
• MATH 7400 - Multidimensional Statistics
• MATH 7420 - Advanced Probability Theory II
• MATH 7430 - Topics in Probability
• MATH 7480 - Topics in Statistics
• MATH 7580 - Computational Statistics
• MATH 7590 - Generalized Linear Models and Extensions
• other MATH 600-7000 level or STAT 6000-7000 level letter-graded courses approved by the graduate coordinator

Additional Statistics Elective. Select courses from STAT or MATH

Other Requirements

Qualifying Exam and Preliminary Exam

Culminating Experience (16 credits)

• MATH 7990 - Dissertation Research

Minimum Total Credits (60 credits)

Additional requirements.

• Minimum 3.0 graduate cumulative grade point average
• Maximum of 10 credits of 5000-level coursework may be counted toward degree requirements
• Preliminary Examination or Project
• Minimum of  16 credits of dissertation research (maximum of 30 credits of dissertation research are applicable to degree requirements)
• Dissertation Defense and Publication of Manuscript on OhioLINK
• All requirements must be completed within eight years from the end of the earliest course used to fulfill degree requirements.

PhD Estimate and field statistics for elasto-dissipative composite (M/F)

Job Information

Offer description.

The thesis will be carried out at the Laboratoire de Mécanique et d'Acoustique (LMA), a joint AMU-CNRS-Centrale Méditerranée research unit (UMR 7031). Its main areas of expertise are solid mechanics (structure, materials, interfaces) and acoustics (wave propagation in complex fluid and solid media).

Thesis context : The design of industrial structures made of heterogeneous materials is based on increasingly powerful numerical tools. However, these tools are still often based on phenomenological formulations of behaviour laws that only briefly describe the complex mechanisms active at the scale of microstructures, particularly when the latter couple reversible and irreversible phenomena. Micromechanical (or homogenisation) approaches, based on a limited but sufficient number of local state descriptors, have been developed to construct the macroscopic response of heterogeneous materials, taking into account the properties of the constituent phases and their microstructural morphology. Integrated at the scale of the integration point of a structural calculation, they can lead to a significant saving in calculation time compared with 'finite element squared' methods in which local interactions are described by extremely costly 'full field' calculations. This thesis is funded as part of the ANR AnoHona (Advanced NOnlinear HOmogenization for structural aNAlysis) project, which aims to : – Formulate a generic framework for homogenised behaviour laws and translate it into an open software library that can be interfaced with any structural calculation code (axis 1). – Develop a methodology to improve the description of the actual behaviour of materials with ductile phases, on the one hand by introducing macroscopic variables describing the heterogeneity of local fields in the phases (axis 2), and on the other hand by taking into account general, potentially complex microstructural morphologies (axis 3). – Demonstrate the feasibility of the approach to a real industrial case involving strong non-linearities, multiphysical couplings, a microstructure and complex stresses.

Scientific objectives : This thesis is part of Axis 2 of the project, which aims to propose a mean-field method for estimating the effective properties and statistical fluctuations of local fields in a viscoelastic linear comparison composite (LCC). These estimates can be generated by two families of approaches: direct approaches based mainly on the correspondence principle and variational approaches based on approximations of the microscopic fields. Direct approaches have the advantage of simplicity of implementation and accuracy in estimating the actual behaviour of the LCC, but in the general case they do not allow us to estimate the fluctuations in local fields that are essential for a relevant definition of the LCC. Variational approaches can be used to estimate these statistics but are difficult to implement and have their limitations, particularly for complex loading paths (fatigue, non-radial loading). The aim of this thesis is to develop a method unifying the two approaches for solving the LCC in a viscoelastic framework.

Profile required : Engineer or Master's degree, excellent level in the mechanics of materials, particularly in non-linear mechanics (behaviour models formulated within the framework of the thermodynamics of irreversible processes, viscoelasticity, etc.) and in structural calculations. Knowledge of homogenisation would be a plus.

Requirements

Additional information, work location(s), where to apply.