# Descriptions of Graduate Level Courses

### STAT915 - NONPARAMETRIC INFERENCE

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 520 or equivalent

### STAT920 - SAMPLE SURVEY METHODS

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 520, 961 or 970 or permission of instructor

### STAT921 - OBSERVATIONAL STUDIES

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 520, 961 or 970 or permission of instructor

### STAT925 - MULTIVARIATE ANALY: THEO

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 930, 970 and 972 or permission of instructor

### STAT926 - MULTIVARIATE ANALY: METH

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 961 or permission of instructor

### STAT927 - 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 430 or STAT 510

### STAT928 - STAT LEARNING THEORY

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.

Prerequisites: Probability and linear algebra.

### STAT930 - PROBABILITY THEORY (Course Syllabus)

Measure theory and foundations of Probability theory. Zero-one Laws. Probability inequalities. Weak and strong laws of large numbers. Central limit theorems and the use of characteristic functions. Rates of convergence. Introduction to Martingales and random walk.

Prerequisites: MATH 608

### STAT931 - STOCHASTIC PROCESSES

Markov chains, Markov processes, and their limit theory. Renewal theory. Martingales and optimal stopping. Stable laws and processes with independent increments. Brownian motion and the theory of weak convergence. Point processes.

Prerequisites: MATH 546, STAT 930

### STAT955 - STOCH CAL & FIN APPL

Selected topics in the theory of probability and stochastic processes.

Prerequisites: STAT 930 or equivalent

### STAT961 - 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 431 or 520 or equivalent; a solid course in linear algebra and a programming language

### STAT962 - ADV METHODS APPLIED STAT

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 961

### STAT970 - MATHEMATICAL STATISTICS (Course Syllabus)

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

Prerequisites: STAT 431 or 520 or equivalent; comfort with mathematical proofs (e.g., MATH 360)

### STAT971 - 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 970

### STAT972 - ADV TOPICS IN MATH STAT (Course Syllabus)

A continuation of STAT 970.

Prerequisites: STAT 970 and 971

### STAT974 - 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 102 or 112

### STAT991 - 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.

### STAT999 - INDEPENDENT STUDY

Prerequisites: Written permission of instructor and the department course coordinator.

### Statistics Department

The Wharton School,
University of Pennsylvania
400 Jon M. Huntsman Hall
3730 Walnut Street