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Ph.d. program.

Statistical Science at Duke is the world's leading graduate research and educational environment for Bayesian statistics, emphasizing the major themes of 21st century statistical science: foundational concepts of statistics, theory and methods of complex stochastic modeling, interdisciplinary applications of statistics, computational statistics, big data analytics, and machine learning. Life as a Ph.D. student in Statistical Science at Duke involves immersion in a broad range of research experiences and emphasizes conceptual innovation, as well as building a deep and broad foundation in theory and methods.

Coupled with our core emphases in modeling, computation and the methodologies of modern statistical science is a broad range of interdisciplinary relationships with many other disciplines (biomedical sciences, environmental sciences, genomics, computer science, engineering, finance, neuroscience, social sciences, and others). The rich opportunities for students in interdisciplinary statistical research at Duke are complemented by opportunities for engagement in research in summer projects with nonprofit agencies, industry, and academia.

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Department of Statistics and Data Science

Ph.d. program.

Fields of study include the main areas of statistical theory (with emphasis on foundations, Bayes theory, decision theory, nonparametric statistics), probability theory (stochastic processes, asymptotics, weak convergence), information theory, bioinformatics and genetics, classification, data mining and machine learning, neural nets, network science, optimization, statistical computing, and graphical models and methods.

With this background, graduates of the program have found excellent positions in universities, industry, and government. See the list of alumni for examples.

Bayesian Statistics

A probabilistic framework that integrates prior knowledge with new data to update and refine probability distributions, providing a powerful tool for inference and decision-making.

Veronica Berrocal

Mine dogucu, volodymyr minin, babak shahbaba, weining shen, erik sudderth, recent news about bayesian statistics, summer school for stem faculty: a boot camp in bayesian thinking, professors berrocal and shahbaba named american statistical association fellows.

Doctor of Philosophy in the Field of Statistics (STEM)

Statistics plays an important role throughout society, providing methodologies for advances in medicine, genetics, and other research arenas, and for making decisions in business and public policy. GW's PhD in statistics program provides advanced training in topics including probability, linear models, time series analysis, Bayesian statistics, inference, reliability, statistics in law and regulatory policy, and more. The degree provides training in theory and applications and is suitable for both full- and part-time students. Most graduate courses are offered in the early evening to accommodate student schedules. 

Nearly all GW statistics PhD graduates have secured positions in the statistics or data science industry, with employers including Amazon, Facebook, and Capital One. During the program, students work closely with faculty on original research in their area of interest. 

To be admitted, applicants typically have a master’s degree in statistics or a related discipline. Students need a strong background in mathematics, including courses in advanced calculus, linear algebra, and mathematical statistics.

This is a STEM designated program.

Visit the program website for additional information.

Supporting documents not submitted online should be mailed to:

Columbian College of Arts and Sciences, Office of Graduate Studies The George Washington University 801 22nd Street NW, Phillips Hall 107 Washington DC 20052

For additional information about the admissions process visit the Columbian College  of Arts and Sciences  Frequently Asked Questions  page.

[email protected] 202-994-6210 (phone)

Hours: 9:00 am to 5:00 pm, Monday through Friday

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Bayesian statistics

Persi Diaconis

Bradley Efron

Julia Palacios

Chiara Sabatti

We have 7 Statistics (bayesian statistics) PhD Projects, Programmes & Scholarships

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Statistics (bayesian statistics) PhD Projects, Programmes & Scholarships

Marie-curie (msca) doctoral fellowship: phd in structural dynamics and health monitoring of composite and 3d printed structures and systems, phd research project.

PhD Research Projects are advertised opportunities to examine a pre-defined topic or answer a stated research question. Some projects may also provide scope for you to propose your own ideas and approaches.

Funded PhD Project (Students Worldwide)

This project has funding attached, subject to eligibility criteria. Applications for the project are welcome from all suitably qualified candidates, but its funding may be restricted to a limited set of nationalities. You should check the project and department details for more information.

Bayesian Computation for Modern Slavery Statistics

Competition funded phd project (uk students only).

This research project is one of a number of projects at this institution. It is in competition for funding with one or more of these projects. Usually the project which receives the best applicant will be awarded the funding. The funding is only available to UK citizens or those who have been resident in the UK for a period of 3 years or more. Some projects, which are funded by charities or by the universities themselves may have more stringent restrictions.

Simulation-based inference for financial econometrics models

Competition funded phd project (students worldwide).

This project is in competition for funding with other projects. Usually the project which receives the best applicant will be successful. Unsuccessful projects may still go ahead as self-funded opportunities. Applications for the project are welcome from all suitably qualified candidates, but potential funding may be restricted to a limited set of nationalities. You should check the project and department details for more information.

Bayes factor surface for searches for new physics

The university of manchester - department of mathematics, funded phd programme (students worldwide).

Some or all of the PhD opportunities in this programme have funding attached. Applications for this programme are welcome from suitably qualified candidates worldwide. Funding may only be available to a limited set of nationalities and you should read the full programme details for further information.

Maths Research Programme

PhD Research Programmes describe the opportunities for postgraduate research within a University department. You may often be asked to submit your own research project proposal as part of your application, although predefined research projects may also be available.

Noise and Evolution in Ageing Cellular Power Stations

Competition funded phd project (european/uk students only).

This project is in competition for funding with other projects. Usually the project which receives the best applicant will be successful. Unsuccessful projects may still go ahead as self-funded opportunities.

Modelling the Impact of Diagnostic Pathways in Cancer and Cardiovascular Disease - University of Swansea (part of Health Data Research UK’s Big Data for Complex Disease Driver Programme)

Funded phd project (uk students only).

This research project has funding attached. It is only available to UK citizens or those who have been resident in the UK for a period of 3 years or more. Some projects, which are funded by charities or by the universities themselves may have more stringent restrictions.

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Descriptions of Graduate Level Courses

Stat9150 - nonparametric inference (course syllabus).

Statistical inference when the functional form of the distribution is not specified. Nonparametric function estimation, density estimation, survival analysis, contingency tables, association, and efficiency.

Prerequisites: STAT 5200

STAT9200 - Sample Survey Methods (Course Syllabus)

This course will cover the design and analysis of sample surveys. Topics include simple random sampling, stratified sampling, cluster sampling, graphics, regression analysis using complex surveys and methods for handling nonresponse bias.

Prerequisites: STAT 5200 OR STAT 9610 OR STAT 9700

STAT9210 - Observational Studies (Course Syllabus)

This course will cover statistical methods for the design and analysis of observational studies. Topics will include the potential outcomes framework for causal inference; randomized experiments; matching and propensity score methods for controlling confounding in observational studies; tests of hidden bias; sensitivity analysis; and instrumental variables.

STAT9220 - Advanced Causal Inference (Course Syllabus)

This course will provide an in depth investigation of statistical methods for drawing causal inferences from complex observational studies and imperfect randomized experiments. Formalization will be given for key concepts at the foundation of causal inference, including: confounding, comparability, positivity, interference, intermediate variables, total effects, controlled direct effects, natural direct and indirect effects for mediation analysis, generalizability, transportability, selection bias, etc.... These concepts will be formally defined within the context of a counterfactual causal model. Methods for estimating total causal effects in the context of both point and time-varying exposure will be discussed, including regression-based methods, propensity score techniques and instrumental variable techniques for continuous, discrete, binary and time to event outcomes. Mediation analysis will be discussed from a counterfactual perspective. Causal directed acyclic graphs (DAGs) and associated nonparametric structural equations models (NPSEMs) will be used to formalize identification of causal effects for static and dynamic longitudinal treatment regimes under unconfoundedness and unmeasured confounding settings. This formalization will be used to define, identify and make inferences about the joint effects of time-varying exposures in the presence of (possibly hidden) time-dependent covariates that are simultaneously confounders and intermediate variables. These methods include g-estimation of structural nested models, inverse probability weighted estimators of marginal structural models, and g-computation algorithm estimators. Credible quasi-experimental causal inference methods will be described, leveraging auxiliary variables such as instrumental variables, negative control variables, or more broadly confounding proxy variables. Quasi-experimental methods discussed will include the control outcome calibration approach, proximal causal inference, difference-in-differences and related generalizations of these methods. Semiparametric efficiency and the prospects for doubly robust inference will feature prominently throughout the course, including methods that combine modern semiparametric theory and machine learning techniques.

STAT9250 - Multivariate Analy: Theo (Course Syllabus)

This is a course that prepares PhD students in statistics for research in multivariate statistics and high dimensional statistical inference. Topics from classical multivariate statistics include the multivariate normal distribution and the Wishart distribution; estimation and hypothesis testing of mean vectors and covariance matrices; principal component analysis, canonical correlation analysis and discriminant analysis; etc. Topics from modern multivariate statistics include the Marcenko-Pastur law, the Tracy-Widom law, nonparametric estimation and hypothesis testing of high-dimensional covariance matrices, high-dimensional principal component analysis, etc.

Prerequisites: STAT 9300 OR STAT 9700 OR STAT 9720

STAT9260 - Multivariate Analy: Meth (Course Syllabus)

This is a course that prepares PhD students in statistics for research in multivariate statistics and data visualization. The emphasis will be on a deep conceptual understanding of multivariate methods to the point where students will propose variations and extensions to existing methods or whole new approaches to problems previously solved by classical methods. Topics include: principal component analysis, canonical correlation analysis, generalized canonical analysis; nonlinear extensions of multivariate methods based on optimal transformations of quantitative variables and optimal scaling of categorical variables; shrinkage- and sparsity-based extensions to classical methods; clustering methods of the k-means and hierarchical varieties; multidimensional scaling, graph drawing, and manifold estimation.

Prerequisites: STAT 9610

STAT9270 - Bayesian Statistics (Course Syllabus)

This graduate course will cover the modeling and computation required to perform advanced data analysis from the Bayesian perspective. We will cover fundamental topics in Bayesian probability modeling and implementation, including recent advances in both optimization and simulation-based estimation strategies. Key topics covered in the course include hierarchical and mixture models, Markov Chain Monte Carlo, hidden Markov and dynamic linear models, tree models, Gaussian processes and nonparametric Bayesian strategies.

Prerequisites: STAT 4300 OR STAT 5100

STAT9280 - Stat Learning Theory (Course Syllabus)

Statistical learning theory studies the statistical aspects of machine learning and automated reasoning, through the use of (sampled) data. In particular, the focus is on characterizing the generalization ability of learning algorithms in terms of how well they perform on "new" data when trained on some given data set. The focus of the course is on: providing the fundamental tools used in this analysis; understanding the performance of widely used learning algorithms; understanding the "art" of designing good algorithms, both in terms of statistical and computational properties. Potential topics include: empirical process theory; online learning; stochastic optimization; margin based algorithms; feature selection; concentration of measure. Background in probability and linear algebra recommended.

STAT9300 - Probability Theory (Course Syllabus)

Measure theoretic foundations, laws of large numbers, large deviations, distributional limit theorems, Poisson processes, random walks, stopping times.

Prerequisites: STAT 4300 OR STAT 5100 OR MATH 6080

STAT9310 - Stochastic Processes (Course Syllabus)

Continuation of MATH 6480/STAT 9300, the 2nd part of Probability Theory for PhD students in the math or statistics department. The main topics include Brownian motion, martingales, Ito's formula, and their applications to random walk and PDE.

Prerequisites: MATH 5460 OR STAT 9300

STAT9550 - Stoch Cal & Fin Appl (Course Syllabus)

Selected topics in the theory of probability and stochastic processes.

Prerequisites: STAT 9300

STAT9600 - Stat Algorithms & Comp (Course Syllabus)

This course aims to prepare students for graduate work in the design, analysis, and implementation of statistical algorithms. The target audience is Ph.D. students in statistics or in adjacent fields, such as computer science, mathematics, electrical engineering, computational biology, economics, and marketing. We will take a fundamental approach and focus on classes of algorithms of primary importance in statistics and statistical machine learning. Some meta-classes of algorithms that may receive significant attention are optimization, sampling, and numerical linear algebra. I aim to make the content complementary rather than overlapping with other courses at Penn, such as ESE6050, CIS6770, and the CIS7000 series. While there may be some overlap in the portions of the course that cover optimization, the sampling (Monte Carlo and related) aspects of the course are, to my knowledge, hard to find elsewhere at Penn. The course is fast paced and I expect a certain degree of mathematical preparation. Most students in the above mentioned programs will have the requisite mathematics background. I also expect familiarity with an appropriate programming language such as R, python, or matlab. The course will be mostly language agnostic. However, I may at times give example code in one of these languages, and you will be expected to be able to read the code even if it is not in your "primary" language. We may make use of various open-source toolboxes and packages for these environments, such as the Stan probabilistic programming language (best used with R) and the cvx toolbox for convex programming (available for multiple platforms but perhaps best used with matlab).

STAT9610 - Statistical Methodology (Course Syllabus)

This is a course that prepares 1st year PhD students in statistics for a research career. This is not an applied statistics course. Topics covered include: linear models and their high-dimensional geometry, statistical inference illustrated with linear models, diagnostics for linear models, bootstrap and permutation inference, principal component analysis, smoothing and cross-validation.

Prerequisites: STAT 4310 OR STAT 5200

STAT9620 - Adv Methods Applied Stat (Course Syllabus)

This course is designed for Ph.D. students in statistics and will cover various advanced methods and models that are useful in applied statistics. Topics for the course will include missing data, measurement error, nonlinear and generalized linear regression models, survival analysis, experimental design, longitudinal studies, building R packages and reproducible research.

STAT9700 - Mathematical Statistics (Course Syllabus)

Decision theory and statistical optimality criteria, sufficiency, point estimation and hypothesis testing methods and theory.

STAT9710 - Intro To Linear Stat Mod (Course Syllabus)

Theory of the Gaussian Linear Model, with applications to illustrate and complement the theory. Distribution theory of standard tests and estimates in multiple regression and ANOVA models. Model selection and its consequences. Random effects, Bayes, empirical Bayes and minimax estimation for such models. Generalized (Log-linear) models for specific non-Gaussian settings.

Prerequisites: STAT 9700

STAT9720 - Adv Topics in Math Stat (Course Syllabus)

A continuation of STAT 9700.

Prerequisites: STAT 9700 AND STAT 9710

STAT9740 - Modern Regression (Course Syllabus)

Function estimation and data exploration using extensions of regression analysis: smoothers, semiparametric and nonparametric regression, and supervised machine learning. Conceptual foundations are addressed as well as hands-on use for data analysis.

Prerequisites: STAT 1020 OR STAT 1120

STAT9800 - Intro to Biomed Data Science (Course Syllabus)

This course offers a comprehensive introduction to biomedical data science research, tailored for graduate students from Statistics and various interdisciplinary domains. Aimed at facilitating end-to-end data science research capabilities, this course covers the development and application of computational methods and statistical techniques for analyzing voluminous datasets, particularly in biology, healthcare, and medicine. Students will gain insights into various data types prevalent in biomedical research, emerging large-scale data resources, and the art of formulating scientific questions. The course encompasses methodology research, scientific research, collaborative research, computing tools, software development, as well as scientific writing, including both research papers and grant proposals. By the end of the course, students will be equipped with the foundational skills and knowledge required to excel as statisticians and research scientists, whether they choose to pursue a career in industry or academia. Prerequisite: For students from the STAT department, this course is tailored for those who have successfully completed the qualifying exam and are ready to embark on their research journey. Exceptions for first-year students will be considered on an individual basis. For master's or Ph.D. students from other departments or programs, such as AMCS, the prerequisites will differ based on their specific curriculum. At a minimum, students should have master-level expertise in one or more of the following areas: applied mathematics and probability, computing and software development, web development, bioinformatics, biostatistics, epidemiology, computational biology, genetics/genomics, neuroscience, radiology, and medical imaging.

STAT9910 - Sem in Adv Appl of Stat (Course Syllabus)

This seminar will be taken by doctoral candidates after the completion of most of their coursework. Topics vary from year to year and are chosen from advance probability, statistical inference, robust methods, and decision theory with principal emphasis on applications.

STAT9950 - Dissertation (Course Syllabus)

Stat9990 - independent study (course syllabus).

Written permission of instructor and the department course coordinator required to enroll.

STAT9999 - Independent Study (Course Syllabus)

Department of statistics and data science.

The Wharton School, University of Pennsylvania Academic Research Building 265 South 37th Street, 3rd & 4th Floors Philadelphia, PA 19104-1686

Phone: (215) 898-8222

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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

Associate 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

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

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

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. "

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 Ruixin Dai

Wenxuan Guo

Shunzhuang Huang So Won (Sowon) Jeong Takuya Koriyama

Jizhou Liu Yanlong Liu Edoardo Marcelli Bengusu (Bengu) Nar Chad Schmerling

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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Statistics Doctor of Philosophy

The Department of Statistics offers several graduate degree programs, including the MS and PhD in Statistics and the Master of Applied Statistics (MAS) degree. It jointly administers a unique Interdisciplinary PhD Program in Biostatistics  with the Division of Biostatistics in the College of Public Health.

The department aims to contribute to virtually all areas of statistical science, including the development of novel statistical theory and methodology. Specific areas of excellence include Bayesian statistics, spatio-temporal statistics, statistical learning and biostatistics.

Research is directed toward modern and emerging areas of interest. A large portion of the department’s faculty and students are involved in interdisciplinary research and make significant scientific contributions beyond the field of statistics. Faculty members are highly successful at securing competitive grants from various research funding agencies, including the National Science Foundation (NSF) and National Institutes of Health (NIH). In addition, the department is a partner in administering the NSF-funded  Mathematical Biosciences Institute  on the Ohio State campus.

PhD in Statistics

The core of the PhD program consists of course work in mathematical statistics, as well as a variety of applied and theoretical courses in various topical areas. In the early part of the program, students complete required and elective course work in addition to qualifying examinations. Note that we admit students to the statistics department to work in statistics, but not to work with a particular faculty member. For a student’s first two years in the program, the Graduate Studies Chair of the department serves as the advisor and students are encouraged to take independent study courses with faculty members they might like to work with.

After the second year, students, together with faculty members, decide who will be their PhD dissertation advisor(s) and committee members. After completing the qualifying exams and course work, students focus on research and finish the program with their dissertation and defense. Students typically complete the program in about five years although it is possible to finish in less time, depending on the student’s dissertation progress.

For more information, visit stat.osu.edu .

Optional Practical Training (OPT)

International graduates of this major are approved by the Department of Homeland Security for three (3) years of work permission in the United States after graduation. Visit the Office of International Affairs website for more information.

If you have a disability and experience difficulty accessing this content, please contact [email protected] .

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Graduate Programs

Biostatistics.

The doctoral program in Biostatistics provides the training necessary to carry out independent research in theory, methodology and the application of statistics to important problems in biomedical research, including research biology, public health and clinical medicine.

The Ph.D. program is administered by an active, expanding and highly interdisciplinary faculty in the Department of Biostatistics. Major areas of research activity include Bayesian inference, analysis of biomarkers and diagnostic tests, causal inference and missing data, time series and functional data analysis, modeling of social networks, bioinformatics, longitudinal data, and multilevel modeling. Faculty collaborate actively with investigators in the areas of cancer prevention and screening, behavioral sciences, HIV/AIDS, health care policy, genetic epidemiology, neuroscience, and genomics.

Additional Resources

All PhD graduate students are provided with a new laptop computer and office space.  Students also have access to the computing infrastructure at the Center for Statistical Sciences, a high-end, continuously updated computing environment featuring both Unix and PC/MAC networks, with access to all major software for data analysis and numerical computing. CSS also maintains a considerable collection of statistics texts and journals in the Walter Freiberger Biostatistics Library.

Application Information

MCAT or LSAT tests cannot be substituted for the GRE. Applicants to the Ph.D. program should have taken courses in calculus (three semesters), and advanced undergraduate courses in linear algebra and probability. Experience with numerical computing is also recommended. Applications from students in applied fields such as biology, biochemistry, economics, and computer science are strongly encouraged, with the understanding that necessary mathematical coursework may have to be completed before or soon after enrollment in the program.

Applicants to this School of Public Health program should apply through  SOPHAS , a centralized application service for accredited schools and programs in public health. Brown University School of Public Health GRE reporting code: 7765.

Application Requirements

Gre subject:.

Not required

GRE General:

Official transcripts:, letters of recommendations:.

(3) Required

Personal Statement:

Additional materials:.

Application Fee

Additional Requirements:

International applicants.

• Language Proficiency (TOEFL or IELTS if applicable)
• Transcript Evaluation (if applicable)

Dates/Deadlines

Application deadline, completion requirements.

For all Ph.D. students, 24 credits are required of students matriculating in the program without a master's degree; 16 are required beyond the master's. For those with a related master's degree, up to eight units can be transferred. Both written and oral exams, plus a dissertation comprising an original contribution to the field, also are required. Students are expected to participate in academic activities such as the Statistics Seminar and faculty–organized working groups.

Alumni Careers

Contact and Location

Department of biostatistics, mailing address.

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Research Focus Areas & Applications

Research areas in the Department of Statistics are diverse and multidisciplinary with application areas that range from finance to social sciences.

Research Focus Areas

Bayesian statistics.

Bayesian statistics is an approach to inference based on the celebrated Bayes theorem (ca 1763). It combines one's prior information on the unknown parameters of a model with the observed data to form the so-called posterior distribution, which reflects the updated knowledge on the parameters. Our faculty's expertise span from the development of Bayesian statistical models for complex problems to the study of their theoretical guarantees to aspects of scalable implementation. Areas of particular interest include methodologies for variable selection and regularization, graphical models, probabilistic image analysis, multiscale modeling, network analysis, quantile regression and methods for massive data sets with complex dependence structures, including functional, time series and spatial data. Applied areas of interest include biomedical applications, neuroscience, finance and economics, engineering and industrial applications and material informatics.

• Katherine Ensor
• Daniel Kowal
• Marina Vannucci
• Frederi Viens

Biostatistics and Bioinformatics

Biostatistics addresses statistical problems in biology, medicine and public health. This includes epidemiology, clinical trials, survival analysis, and biomedical imaging. Biological and medical problems that deal with large genetic datasets or the complex nature of how genes interact or communicate with each other and their environment come under bioinformatics, statistical genetics, or systems biology. Department faculty and joint faculty from M.D. Anderson Cancer Center are leaders in the development and application of biostatistical and genomic methods, many of which are motivated by modern problems involving big data, high dimensions and complex structures. Methods that can be used to address these problems include data integration, prediction, statistical machine learning, Bayesian modeling, causal inference and graphical models.

• Rudy Guerra
• Marek Kimmel

Data Science

Classical multivariate data analysis encompasses data understanding, data visualization, computational statistics, and optimization. Rice Statistics Department researchers have provided groundbreaking research in exploratory data analysis and nonparametric methodology. Advanced functional visualization facilitates discovery of the unexpected. New emphasis on computational efficiency and convex optimization permit analyses of big data.  All of these ideas have evolved into modern Data Science, with its ability to formulate complex models to extract knowledge using interdisciplinary research in deep learning and data mining.  Together with its partners in the Engineering School, the Department of Statistics is leading the way towards the next big discoveries.

• Loren Hopkins
• Erzsébet Merényi

Dependent Data

Dependent data is the term used when observations are collected in a way that constrains their randomization. Examples include time series and panel data, spatial and spatial-temporal methods and image analysis. Further, analyses based on advanced study designs such as stratified, cluster and cohort sampling require advanced methods in dependent data. Functional data is another type of dependent data. Rather than observing individual points, the data itself may be functions. Functional methods provide a modern solution to capitalize on the distinctive nature of dependent data. Stochastic processes are also central to methodological development in this arena. Faculty working in this area also address questions related to causal inference.

• John Dobelman

Foundations of Probability and Statistics

In Statistics there is often no single correct way to analyze a data set or answer a scientific question. Many methods of statistical inference are based on probability models, and finding an appropriate model depends on a deep understanding of probability theory. Theoretical statistics incorporates more than just probability modeling in its quest to squeeze all information from a data set. Researchers at Rice have contributed to understanding probability models and their application in numerous fields including finance, population genetics, and biological systems. They have also made breakthroughs in statistical methodologies for many new types of complex data sets that arise in environmental engineering, biomedical research, and other areas.

Multivariate Analysis, Machine Learning, Graphical Models

Data sets arising in artificial intelligence, machine learning, computational social science, genomics, and other areas are huge and varied. Statistical learning from massive and multidimensional data leverages powerful mathematical methods, including low- and high-dimensional graphical models and supervised and unsupervised learning methods dating back to the 1890s. The faculty of the statistics department has developed cutting-edge statistical learning methods for modern multidimensional data, with applications ranging from neuroscience to public health and social networks.

Nonparametrics

Faculty are developing nonparametric methods for situations where the data cannot be assumed to come from a distribution described by a fixed functional form controlled by a small number of parameters. This is common for modern big data scenarios characterized by large sample size, large number of variables, mixed variables, and complex multi-modal structure. Faculty in the Department address these challenges by developing novel data-driven and machine learning approaches, including density estimation, regression,  latent variable methods, clustering, classification, neural map manifold learning, Gaussian Processes, Dirichlet processes, and Neural Networks. The Department’s research has contributed to the advancement of many applications using these methods, including cancer studies, neuroscience diagnosis from medical imagery, EEG, EMG, and other medical data; financial modelling; social science investigations; compositional analysis of planetary surfaces from hyperspectral imagery; discovery from astronomical imagery.

Probability and Stochastic Processes

Probability and stochastic processes provide the mathematical foundation for studying phenomena that evolve stochastically, often over time or space. Our faculty’s cutting edge research is focused on solving real-world problems which can be appropriately modelled in a stochastic framework. This focus permeates many subfields of stochastic analysis, including optimal stopping and optimal stochastic control for problems in mathematical finance and portfolio optimization, branching processes for the progression of cancerous tumors, optimal detection of hidden targets for military applications, quickest detection problems for deep space applications, and statistical inference for stochastic processes with long-memory. 

Applications

Astronomy, and earth and planetary remote sensing.

Spectrally highly resolved measurements of materials in image context –hyperspectral imagery -are an indispensable type of big data today. Modern hyperspectral sensors record repeatable information with unprecedented detail on geologic properties, environmental conditions, urban characteristics, plant species and health, and more (for planetary surfaces), and on the composition and kinematics of protoplanetary disks, where new planets are born, or giant molecular clouds where stars are born, among many other uses. Exploitation of the resulting high-dimensional, large data sets with extremely complex structure and often very few labeled samples poses new mathematical and statistical challenges. Work in the Department has been addressing these challenges by novel clustering, classification and regression methods in multidisciplinary collaborations and has made scientific advances in understanding Earth, Mars, Pluto, asteroids. Recent projects with Rice’s Physics and Astronomy Department have been focusing on Machine Intelligence tools for discovery from the world’s most advanced hyperspectral telescope, ALMA; and for Dark Matter search from the most advanced astroparticle detector experiment, XENON.

Biomedical 

From its beginnings in 1987, the Statistics Department was engaged in development of mathematical and statistical tools for cancer research, epidemics, cardiovascular medicine, medical imaging and others. This includes development of probability and statistical methodologies, computational algorithms, and specific applications. Strong collaborations with MD Anderson Biostatistics and, more recently, Bioinformatics and Computational Biology, as well as with Molecular and Human Genetics and other departments at Baylor College of Medicine, have resulted in lasting relationships and the generation of external support for research and the graduate training. One of the achievements is the Joint PhD Program in Biostatistics between Rice and MD Anderson, which will soon celebrate 20 years of existence. It is supported by an NCI T32 Training Grant. Department graduates in this area have successfully obtained positions as (a) faculty in top academic institutions, such Harvard, Johns Hopkins, Mayo Clinic, University of Michigan, MD Anderson, BCM, University of Manchester, and (b) senior researchers in GlaxoSmithKline, Sanofi and NASA Life Science, among other places. 

Data/Statistical Engineering 

Today’s statistical data scientists find the need to develop end-to-end scientifically sound statistical solutions to often complex and ill formed problems. The idea is not specific to an area, but rather a willingness to actively engage in the collaborative process of engineering innovative solutions. Examples from the statistics department in this area include: energy exploration and production; geosteering (the process of adjusting the drill’s direction in real time based on geological logging measurements); improved flood management; the Urban Data Platform (kinderudp.org) for the greater Houston area, among others.

The Department plays a key role in the study of computational finance through the Center for Computational Finance and Economic Systems (CoFES).  CoFES is dedicated to the quantitative study of financial markets and  their ultimate impact on society. CoFES represents Rice University’s commitment to this important area of intellectual inquiry, and is a cooperative effort between the George R. Brown School of Engineering, the  School of Social Science and the Jesse H. Jones School of Business.  Through research and education CoFES will advance the boundaries of  modeling and computational science in this important arena. A key component of the center is the integration of probabilistic and statistical modeling for complex, multidisciplinary investigations. Rice University is well suited for this endeavor because of its exceptionally bright student body; its distinguished faculty in engineering, statistics, business and economics; its world-class resources in high-performance computing; and an unusually flexible and collegial environment in which to pursue interdisciplinary research and education.

Neuroscience and Neuroimaging

In the last two decades, the development of a number of innovative technologies has led to an improved understanding of the mechanisms underlying the functioning and disruption of the human brain. In this highly interdisciplinary area, Rice statisticians are developing new models and tools that can help clinicians understand, monitor, and augment brain processes. A particular focus has been in understanding the role that brain connectivity patterns play in neurological and mental health disorders. Rice faculty have developed new models and algorithmic tools to analyze complex data, including images of multi-modalities, omics data, times series, networks and trees. Such data-driven solutions provide insightful understanding of the principles that govern physiology, behavior, cognition, and neurodegenerative diseases.

Social Sciences

Research in the social sciences centers on the study of human behavior, social environments, and interpersonal relationships. Statistical tools are impactful for many broad and important fields in the social sciences, including economics, education, law, political science, international relations, and psychology, among many others. Our faculty offer expertise in core statistical methods for the social sciences, such as cluster analysis, factor models, longitudinal, time series, and functional data analysis, multivariate methods, network analysis, and survey sampling. 

The emerging area of Urban Analytics, brings the best of statistical data science to sustainable development and cities. Focusing on residents of a community, urban analytics advances understanding of how people live, work, learn and play in their respective communities and often requires strong partnerships between academia, local governments and community leaders. 

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Bayesian Statistics - 625.665

In Bayesian statistics, inference about a population parameter or hypothesis is achieved by merging prior knowledge, represented as a prior probability distribution, with data. This prior distribution and data are merged mathematically using Bayes’ rule to produce a posterior distribution, and this course focuses on the ways in which the posterior distribution is used in practice and on the details of how the calculation of the posterior is done. In this course, we discuss specific types of prior and posterior distributions, prior/posterior conjugate pairs, decision theory, Bayesian prediction, Bayesian parameter estimation and estimation uncertainty, and Monte Carlo methods commonly used in Bayesian statistical inference. Students will apply Bayesian methods to analyze and interpret several real-world data sets and will investigate some of the theoretical issues underlying Bayesian statistical analysis. R is the software that will be used to illustrate the concepts discussed in class. Course Note(s): Prior experience with R is not required; students not familiar with R will be directed to an online tutorial.

Course Prerequisite(s)

Multivariate calculus, familiarity with basic matrix algebra, and a graduate course in probability and statistics (such as EN.625.603 Statistical Methods and Data Analysis).

Course Offerings

There are no sections currently offered, however you can view a sample syllabus from a prior section of this course.

* PhD position in Statistical Learning and Uncertainty Quantifications *

Dec 27, 2022

Being Europe’s densest university landscape, the metropolis Ruhr offers attractive career opportunities for excellent scientists and scholars from any part of the world. In 2021, the Ruhr-Universität Bochum, TU Dortmund University and the University of Duisburg- Essen founded the Research Alliance Ruhr to bundle their top international research on grand challenges of humankind. Four research centers and a college will be established in the next three years. This is just the latest chapter of our long-standing cooperation as University Alliance Ruhr (UA Ruhr), a community of 1,300 researchers and 120,000 students in the center of Germany. As part of the Research Alliance Ruhr, the Chair of Uncertainty Quantification and Statistical Learning at the Research Center Trustworthy Data Science and Security and the Department of Statistics at TU Dortmund bridges the gaps between Uncertainty Quantification, Statistical and Machine Learning, and Interdisciplinary Applications. The chair is hiring a PhD position to be filled for the period of 3 years (extension possible) as early as possible. Payment according to public service´s agreement: TV-L E13. The position is full-time, part-time is possible.

Your Expertise and Interests

* Statistical Learning, Bayesian Computational Methods * Uncertainty Quantification in Statistics & Machine Learning * Regularization & Smoothing, Variable Selection & Model Choice * Flexible Regression/Supervised Learning & Spatial Statistics

Your Qualification * Excellent degree (Master of Science) in statistics, mathematics, data science, computer science, or similar programs. * High degree of creativity, commitment, analytical competence, and interdisciplinary teamwork. * High proficiency in English, both written and spoken for your scientific publications and presentations.

What We Offer We work in a multidisciplinary team on collaborative research projects jointly supervised by leading international experts from different domains. We aim at both theoretical research as well as practical applications in close collaboration with academic and industrial partners. The positions are embedded in a creative, attractive, and internationally renowned research environment. With your research and contribution to teaching you will play a primary role in the development of our new Research Center and outreach with trustworthy technology to the public. During your PhD, participation in international conferences and voluntary exchange programs are highly encouraged. Our international network of researchers and industry partners ensures a seamless transition into your next career step. A balanced and family- friendly work-life relationship is important to us, thus we offer options for flexible working times or part-time remote home-office. More Information Further information about the Research Center can be found at: www.rc-trust.ai If you have any further questions, please contact: Prof. Dr. Nadja Klein [email protected] https://rc-trust.ai/klein/

Research Alliance Ruhr The Research Alliance Ruhr is a cooperation of the three major universities in the Ruhr region, which has been initiated by the Ruhr Conference. The four research centers will focus on “One Health – from Molecules to Systems,” “Chemical Sciences and Sustainability,” “Trustworthy Data Science and Security,” and “Future Energy Materials and Systems. In addition, a “College for Social Sciences and Humanities” is being established.

Your Application If you are interested in the position, please send your application (as a single pdf with at least 10MB) until 31st January 2023 via mail to [email protected] Research Center Trustworthy Data Science and Security, UA Ruhr and Department of Statistics, Technische Universität Dortmund Chair of Uncertainty Quantification and Statistical Learning Prof. Dr. Nadja Klein Please provide the usual documents: motivation letter, CV, and copies of your certificates

Career Opportunities Our Research Center will hire 12 research professors in the next few years and offer numerous positions for research assistants and research group leaders. Join us now to create trustworthy innovations for the digital world of tomorrow in Europe’s largest metropolitan region.

Diversity The TU Dortmund University aims to increase the percentage of women in the scientific faculties and therefore, applications from women are particularly welcome. We explicitly note that applications of severely disabled persons are welcome.

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Stanford Online

Bayesian statistics.

Stanford School of Humanities and Sciences

Note : STATS270 is not being offered in the academic year 2024-2025.

This course will treat Bayesian statistics at a relatively advanced level. Assuming familiarity with standard probability and multivariate distribution theory, we will provide a discussion of the mathematical and theoretical foundation for Bayesian inferential procedures. In particular, we will examine the construction of priors and the asymptotic properties of likelihoods and posterior distributions. The discussion will include but will not be limited to the case of finite dimensional parameter space. There will also be some discussions on the computational algorithms useful for Bayesian inference.

Note : This course is cross listed with STATS370 and requires a high level of math knowledge.

Prerequisites

• A conferred Bachelor’s degree with an undergraduate GPA of 3.3 or better
• Theory of probability ( STATS116 ) or equivalent 
• Recommended: Introduction to Statistical Inference ( STATS200 ) or equivalent
• Basic calculus, analysis and linear algebra, and basic knowledge of programming strongly recommended

We strongly recommend that you review the first problem set before enrolling. If this material looks unfamiliar or too challenging, you may find this course too difficult.

What You Need To Get Started

Before enrolling in your first graduate course, you must complete an online application .

Don’t wait! While you can only enroll in courses during open enrollment periods, you can complete your online application at any time.

Once you have enrolled in a course, your application will be sent to the department for approval. You will receive an email notifying you of the department's decision after the enrollment period closes. You can also check your application status in your my stanford connection account at any time.

Learn more about the graduate application process .

How Much It Will Cost

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Seminar Series: Thomas Metzger

Speaker: Thomas Metzger, Department of Statistics, OSU

Title: Bayesian Model Selection with Latent Group-Based Effects and Variances with the R Package slgf

Abstract: In the first part of my talk, I will present the R package slgf which enables the user to easily implement my linear modeling approach to detect latent group-based regression effects, interactions, and/or heteroscedastic error variance through Bayesian model selection. I will focus on the scenario in which the levels of a categorical predictor exhibit two latent groups, treating the detection of this grouping structure as an unsupervised learning problem by searching the space of possible groupings of factor levels.

In the second part, I will discuss approaches to integrating statistical consulting into a well-rounded graduate-level statistics curriculum. Such programs often emphasize technical instruction in theory and methodology but can fail to provide adequate practical training in applications and collaboration skills. I argue that a statistical collaboration center (“stat lab”) is an effective mechanism for providing graduate students with the necessary training in technical, non-technical, and job-related skills. I provide evidence of its positive impact on students via analyses of a survey completed by 123 collaborators who worked in the Laboratory for Interdisciplinary Statistical Analysis (LISA) between 2008–15 while it was housed at Virginia Tech.