**The Wharton School and the University of Pennsylvania must reserve the right to make changes affecting policies, fees, curricula**, or any other matters announced here. Course descriptions represent courses expected to be offered during the 2013-2014 academic year.

While the School endeavors to offer as many of the courses as possible, not all courses are offered every semester. It is important to check with individual departments prior to scheduling classes to determine the availability of courses for any given semester.

**STAT 430: Probability**

Staff, Fall, Spring, & Summer I

*Prerequisite: MATH 114 or equivalent *

Discrete and continuous sample spaces and probability; random variables, distributions, independence; expectation and generating functions; Markov chains and recurrence theory.

**STAT 431: Statistical Inference**

Staff, Fall, Spring, & Summer II

*Prerequisite: STAT 430 *

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. This course does not have business applications but has significant overlap with STAT 101 and 102.

**STAT 433: Stochastic Processes**

Professor Dean Foster, Spring

*Prerequisite: STAT 430 or permission of instructor *

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.

**STAT 500: Applied Regression and Analysis of Variance**

Professor Paul Rosenbaum, Fall

*Prerequisite: STAT 102 or STAT 112 or equivalent*

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.

**STAT 501: Introduction to Nonparametric Methods and Log-linear Models**

Professor Paul Rosenbaum, Spring

*Prerequisite: STAT 102 or STAT 112 or equivalent *

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 non-normal data. Emphasis is on practical methods of data analysis and their interpretation. Primarily for doctoral students in the managerial, behavioral, social and health sciences. May be taken before STAT 500 with permission of instructor.

**STAT 502: Survey Methods and Design**

Professor Robert Boruch, Spring

*Prerequisite: STAT 520 or equivalent *

Methods and design of field surveys in education, the social sciences, criminal justice research, and other areas. It treats methods of eliciting information through household, mail and telephone surveys, methods of assuring privacy, enhancing cooperation rates and related matters. Fundamentals of statistical sampling and sample design are covered. Much of the course is based on contemporary surveys sponsored by the National Center for Education Statistics and other federal, state, and local agencies.

**STAT 510: Probability**

Professor Lawrence Brown, Fall & Summer I

*Prerequisite: A one-year course in calculus *

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.

**STAT 512: Mathematical Statistics**

Staff, Spring

*Prerequisite: STAT 430 or STAT 510 equivalent *

An introduction to the mathematical theory of statistics. Estimation, with a focus on properties of sufficient statistics and maximum likelihood estimators. Hypothesis testing, with a focus on likelihood ratio tests and the consequent development of “t” tests and hypothesis tests in regression and ANOVA. Nonparametric procedures.

**STAT 520: Applied Econometrics I**

Professor Paul Shaman, Fall

*Prerequisites: MATH 114 or equivalent and an undergraduate introduction to probability and statistics*

This is a graduate course in applied econometrics. Topics include multiple linear regression, the bootstrap, quantile regression, instrumental variables, maximum likelihood and probit regression.

**STAT 521: Applied Econometrics II**

Professor Paul Shaman, Spring

*Prerequisite: STAT 520*

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 ordinary least squares estimation, the bootstrap and jackknife, instrumental variables, systems of equations, M-estimation, maximum likelihood, the generalized method of moments, discrete response models, and time series analysis.

**STAT 530: Probability**

Professor Robin Pemantle, Fall

*Prerequisite: STAT 430 or STAT 510 equivalent *

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.

**STAT 531: Stochastic Processes**

Professor Robin Pemantle, Spring

*Prerequisite: STAT 530 *

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.

**STAT 541: Statistical Methodology**

Professor Andreas Buja, Fall

*Prerequisites: STAT 431 or 520 or equivalent; a solid course in linear algebra and a programming language*

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.

**STAT 542: Bayesian Methods and Computation **

Professor Shane Jensen, Spring

*Prerequisites: STAT 430 or 510 or equivalent. *

Sophisticated tools for probability modeling and data analysis from the Bayesian perspective. Hierarchical models, optimization algorithms and Monte Carlo simulation techniques.

**STAT 550: Mathematical Statistics**

Professor Dylan Small, Fall.

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

Decision theory and statistical optimality criteria, sufficiency, invariance, estimation and hypothesis testing theory, large sample theory, information theory.

**STAT 551: Introduction to Linear Statistical Models**

Professor Lawrence Brown, Spring.

*Prerequisite: STAT 550. *

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.

**STAT 552: Advanced Topics in Mathematical Statistics**

Professor Tony Cai, Fall.

*Prerequisites: STAT 550 and STAT 551.*

A continuation of STAT 550.

**STAT 900: Advanced Probability**

Staff. Not offered every year.

*Prerequisite: STAT 531 or equivalent.*

The topics covered will change from year to year. Typical topics include the theory of large deviations, percolation theory, particle systems, and probabilistic learning theory.

**STAT 901: Stochastic Processes II **

Staff. Not offered every year.

*Prerequisite: OPIM 930 or equivalent.*

Martingales, optimal stopping, Wald’s lemma, age-dependent branching processes, stochastic integration, Ito’s lemma.

**STAT 910: Forecasting and Time Series Analysis **

Professor Robert Stine, Spring, odd-numbered years.

*Prerequisite: STAT 520 or 541 or equivalent.*

Fourier analysis of data, stationary time series, properties of autoregressive moving average models and estimation of their parameters, spectral analysis, forecasting. Discussion of applications to problems in economics, engineering, physical science, and life science.

**STAT 915: Nonparametric Inference **

Staff. Not offered every year.

*Prerequisite: STAT 520 or equivalent. *

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

**STAT 920: Sample Survey Methods**

Professor Dylan Small, Not offered every year.

*Prerequisite: STAT 520, 541 or 550 or permission of instructor*

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 non-response bias.

**STAT 921: Observational Studies**

Professor Dylan Small, Fall

*Prerequisite: STAT 520, 541 or 550 or permission of instructor*

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.

**STAT 924: Advanced Experimental Design **

Staff. Not offered every year.

*Prerequisite: STAT 552. *

Factorial designs, confounding, incomplete blocks, fractional factorials, random and mixed models, and response surfaces.

**STAT 925: Multivariate Analysis: Theory**

Professor Zongming Ma, Not offered every year.

*Prerequisites: STAT 550 and linear algebra. *

Tests on mean vectors, discriminant analysis, multivariate analysis of variance, canonical correlation, principal components, and factor analysis.

**STAT 928: Statistical Learning Theory**

Professor Alexander Rakhlin, Not offered every year.

*Prerequisites: Probability and linear algebra. *

Statistical learning theory studies the statistical aspects of machine learning and automated reasoning, through the use of (sampled) data. Potential topics include: empirical process theory; online learning; stochastic optimization; margin based algorithms; feature selection; and concentration of measure.

**STAT 932: Survival Models and Analysis Methods for Medical and Biological Data**

Professor Linda Zhao.

*Prerequisite: STAT 551. *

Parametric models, nonparametric methods for one-and two-sample problems, proportional hazards model, inference based on ranks. Problems will be considered from clinical trials, toxicology and tumorigenicity studies, and epidemiological studies.

**STAT 933: Analysis of Categorical Data**

Professor Paul Rosenbaum.

*Prerequisites: STAT 541 and 551.*

Likelihood equations for log-linear models, properties of maximum likelihood estimates, exact and approximate conditional inference, computing algorithms, weighted least squares methods, and conditional independence and log-linear models. Applied topics, including interpretation of log-linear and logit model parameters, smoothing of tables, goodness-of-fit, and incomplete contingency tables.

**STAT 940: Advanced Inference I **

Staff, Not offered every year.

*Prerequisite: STAT 551. *

The topics covered will change from year to year. Typical topics include sequential analysis, nonparametric function estimation, robustness, bootstrapping and applications decision theory, likelihood methods, and mixture models.

**STAT 941: Advanced Inference II**

Staff, Not offered every year.

*Prerequisite: STAT 940. *

A continuation of STAT 940.

**STAT 950: Quantitative Consulting Seminar**

Professor Richard Waterman, Spring.

No prerequisites, but please talk to the instructor to determine your fit with the course.

The Practicum offers the opportunity for small combined teams of PhD and MBA students to work on “real life” quantitative consulting projects. These projects are drawn from both business and University sources. The emphasis is on providing a relevant and comprehensible solution to the client’s problem. In-class brainstorming sessions, client presentations and written reports give students the opportunity to test for the existence of an intersection between their quantitative and communication skills.

**STAT 955: Stochastic Calculus and Financial Applications **

Professor J. Michael Steele, Fall.

*Prerequisite: STAT 900. *

Selected topics in the theory of probability and stochastic processes.

**STAT 991: Seminar in Advanced Application of Statistics**

Staff, Fall & Spring.

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 advanced probability, statistical inference, robust methods, and decision theory with principal emphasis on applications.