Graduate-Level Courses Descriptions

STAT5000 - Applied Reg & Analy Var (Course Syllabus)

An applied graduate level course in multiple regression and analysis of variance for students who have completed an undergraduate course in basic statistical methods. Emphasis is on practical methods of data analysis and their interpretation. Covers model building, general linear hypothesis, residual analysis, leverage and influence, one-way anova, two-way anova, factorial anova. Primarily for doctoral students in the managerial, behavioral, social and health sciences. Permission of instructor required to enroll.

STAT5010 - Int To Nonp & Loglin Mod (Course Syllabus)

An applied graduate level course for students who have completed an undergraduate course in basic statistical methods. Covers two unrelated topics: loglinear and logit models for discrete data and nonparametric methods for nonnormal data. Emphasis is on practical methods of data analysis and their interpretation. Primarily for doctoral students in the managerial, behavioral, social and health sciences. Permission of instructor required to enroll.

STAT5030 - Data Analy & Stat Comp (Course Syllabus)

This course will introduce a high-level programming language, called R, that is widely used for statistical data analysis. Using R, we will study and practice the following methodologies: data cleaning, feature extraction; web scrubbing, text analysis; data visualization; fitting statistical models; simulation of probability distributions and statistical models; statistical inference methods that use simulations (bootstrap, permutation tests). Prerequisite: Two courses at the statistics 4000 or 5000 level.

STAT5100 - Probability (Course Syllabus)

Elements of matrix algebra. Discrete and continuous random variables and their distributions. Moments and moment generating functions. Joint distributions. Functions and transformations of random variables. Law of large numbers and the central limit theorem. Point estimation: sufficiency, maximum likelihood, minimum variance. Confidence intervals. A one-year course in calculus is recommended.

STAT5110 - Statistical Inference (Course Syllabus)

Graphical displays; one- and two-sample confidence intervals; one- and two-sample hypothesis tests; one- and two-way ANOVA; simple and multiple linear least-squares regression; nonlinear regression; variable selection; logistic regression; categorical data analysis; goodness-of-fit tests. A methodology course.

Prerequisites: STAT 5100

STAT5150 - Adv Stat Inference I (Course Syllabus)

STAT 5150 is aimed at first-year Ph.D. students and builds a good foundation in statistical inference from the first principles of probability.

Prerequisites: STAT 4300 AND STAT 4310 AND MATH 2400

STAT5160 - Adv Stat Inference II (Course Syllabus)

STAT 5160 is a natural continuation of STAT 5150, and the main focus is on asymptotic evaluations and regression models. Time permitting, it also discusses some basic nonparametric statistical methods.

Prerequisites: STAT 5150

STAT5200 - Applied Econometrics I (Course Syllabus)

This is a course in econometrics for graduate students. The goal is to prepare students for empirical research by studying econometric methodology and its theoretical foundations. Students taking the course should be familiar with elementary statistical methodology and basic linear algebra, and should have some programming experience. Topics include conditional expectation and linear projection, asymptotic statistical theory, ordinary least squares estimation, the bootstrap and jackknife, instrumental variables and two-stage least squares, specification tests, systems of equations, generalized least squares, and introduction to use of linear panel data models.

Prerequisites: (MATH 1080 OR MATH 1410) AND MATH 3120

STAT5210 - Applied Econometrics II (Course Syllabus)

Topics include system estimation with instrumental variables, fixed effects and random effects estimation, M-estimation, nonlinear regression, quantile regression, maximum likelihood estimation, generalized method of moments estimation, minimum distance estimation, and binary and multinomial response models. Both theory and applications will be stressed.

Prerequisites: STAT 5200

STAT5330 - Stochastic Processes (Course Syllabus)

An introduction to Stochastic Processes. The primary focus is on Markov Chains, Martingales and Gaussian Processes. We will discuss many interesting applications from physics to economics. Topics may include: simulations of path functions, game theory and linear programming, stochastic optimization, Brownian Motion and Black-Scholes.

Prerequisites: STAT 5100

STAT5350 - Forecasting Methods Mgmt (Course Syllabus)

This course provides an introduction to the wide range of techniques available for statistical modelling and forecasting of time series. Regression methods for decomposition models, trends and seasonality, spectral analysis, distributed lag models, autoregressive-moving average modeling, forecasting, exponential smoothing, and ARCH and GARCH models will be surveyed. The emphasis will be on applications, rather than technical foundations and derivations. The techniques will be studied critically, with examination of their usefulness and limitations.

STAT5440 - Applied Bayesian Modeling (Course Syllabus)

This is a 5000-level graduate course that focuses on the application of statistical techniques from a Bayesian perspective. It is designed for high-level senior undergraduate students who have completed course 4420, as well as for graduate students from various non-statistics fields interested in applying Bayesian methods to their research. The curriculum begins with a refresher on Bayesian statistical principles, followed by practical applications using established software like Stan for model sampling. Critical subjects included in the course are Bayesian model selection, Stan programming, BRMS, variational Bayes methods, regression and mixed effects models, hierarchical structures, dynamic linear models, survival analysis, Gaussian processes, and explorations in nonparametric Bayesian approaches.

Prerequisites: STAT 5100 OR STAT 9300

STAT5710 - Modern Data Mining (Course Syllabus)

Modern Data Mining: Statistics or Data Science has been evolving rapidly to keep up with the modern world. While classical multiple regression and logistic regression technique continue to be the major tools we go beyond to include methods built on top of linear models such as LASSO and Ridge regression. Contemporary methods such as KNN (K nearest neighbor), Random Forest, Support Vector Machines, Principal Component Analyses (PCA), the bootstrap and others are also covered. Text mining especially through PCA is another topic of the course. While learning all the techniques, we keep in mind that our goal is to tackle real problems. Not only do we go through a large collection of interesting, challenging real-life data sets but we also learn how to use the free, powerful software "R" in connection with each of the methods exposed in the class. Prerequisite: two courses at the statistics 4000 or 5000 level or permission from instructor.

STAT5800 - Adv Stat Computing (Course Syllabus)

This course covers the underlying computational methods that both underlie modern statistical and machine learning tools, as well as explicitly computational approaches to performing statistical methods. The class will cover the basics of computer arithmetic, simulation, bootstrap, jackknife and permutation methods, numerical methods for optimization and their application to statistical estimation and machine learning, nonparametric smoothing, generating random variables, and simulation methods. The course will assume familiarity with programming in the R computing environment. By the end of the course, students should be able to design and code estimation methods for sophisticated statistical models, as well as procedures to provide uncertainty about those estimates

Prerequisites: (STAT 1110 OR STAT 1120 OR STAT 4310 OR ESE 4020) AND (STAT 4300 OR ESE 3010) AND (MATH 1080 OR MATH 1410 OR MATH 1610) AND (MATH 2400 OR MATH 3120 OR MATH 3140)

STAT5810 - Conv Optim Stat Data Sci (Course Syllabus)

Convex optimization has become a real pillar of modern data science and has transformed algorithm designs. A wide spectrum of problems in statistics, machine learning, and engineering can be formulated as optimization tasks that exhibit favorable convexity properties, which admit standardized and efficient solutions. This course aims to introduce the elements of convex optimization, concentrating on modeling aspects and algorithms that are useful in data science applications. Topics include convex sets, convex functions, linear and quadratic programs, semidefinite programming, optimality conditions and duality theory. We will visit important applications in statistics and machine learning to demonstrate the wide applicability of convex optimization. We will also cover effective optimization algorithms like gradient descent and Newton's method. Prerequisites: Basic linear algebra, basic calculus, basic probability, and knowledge of a programming language like MATLAB or Python to conduct simulation exercises.

STAT5850 - Foundations of Deep Learning (Course Syllabus)

This course serves as a first, conceptual introduction to Deep Learning, which is the technology at the heart of modern AI. Topics include: what is a neural network and how to train it, generative AI, failure modes and safety of deep learning, and efficient deep learning. Prerequisites: Calculus, beginner programming experience with Python. Highly recommended: basic linear algebra (matrices and matrix multiplication).

STAT5900 - Causal Inference (Course Syllabus)

Questions about cause are at the heart of many everyday decisions and public policies. Does eating an egg every day cause people to live longer or shorter or have no effect? Do gun control laws cause more or less murders or have no effect? Causal inference is the subfield of statistics that considers how we should make inferences about such questions. This course will cover the key concepts and methods of causal inference rigorously. Background in probability and statistics; some knowledge of R is recommended.

STAT5920 - Community Data Science (Course Syllabus)

This course provides students with the opportunity to hone their data science skills and gain practical experience by working with a community organization on a data science problem of interest to the organization. Students will gain skills in problem formulation, collaboration with community organizations and communication of data science results. Students will work in groups of 3-5 on a data science problem of interest to a community organization. This is an Academically Based Community Service (ABCS) course. Prerequisite: The course presumes that students have taken a sequence of introductory statistics courses such as STAT 1010/1020, or 4300/4310 and that they have taken a course that has exposed them to more advanced techniques such as STAT 4220, 4230, 4420, 4710 or 4730. It will be assumed that students have knowledge of a statistical programming language such as R or Python. Classes such as STAT 4050, 4700, 4770 or 4800 would meet this requirement.

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.

Prerequisites: STAT 5200 OR STAT 9610 OR STAT 9700

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.

Prerequisites: STAT 9210 OR BSTA 7900

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.

Prerequisites: STAT 9610

STAT9700 - Mathematical Statistics (Course Syllabus)

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

Prerequisites: STAT 4310 OR STAT 5200

STAT9710 - Theory of Statistics (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 is for graduate students who wish to learn about current research frontiers. It covers advanced topics in probability, statistical theory and methods, applied statistics, data science and artificial intelligence. Specific topics vary from year to year and emphasize both theoretical foundations and applications.

STAT9911 - Sem in Adv Appl of Stat (ML) (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.

STAT9912 - Sem in Adv Appl of Stat (OPT) (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.

STAT9913 - Sem in Adv Appl of Stat (Prob) (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.

STAT9914 - Sem in Adv Appl of Stat (MAST) (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.

STAT9915 - Sem in Adv Appl of Stat (Course Syllabus)

This seminar-based course provides students with the opportunity to hone their data science skills and gain practical experience by working with a community organization on a data science problem of interest to the organization. Students will gain skills in problem formulation, collaboration with community organizations and communication of data science results. Students will work in groups on a data science problem of interest to a community organization.

STAT9916 - 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.

STAT9917 - 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.

STAT9918 - 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)

Dissertation

STAT9999 - Independent Study (Course Syllabus)

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