Required Course Sequence in Statistical Theory

Doctoral students who plan to apply for the AQM certificate may attend an intensive math camp in September — MACS 33000: Computational Math and Statistics – for a review of linear algebra, differential/integral calculus, and probability/statistical theory that constitute the mathematical foundations of quantitative research methods.

AQM students are required to complete SOSC 26006/36006: Foundations for Statistical Theory, STAT 24400: Statistical Theory and Methods I, and STAT 24500: Statistical Theory and Methods II in a sequence. SOSC 26006/36006 may be waived if a student has taken probability and statistical theory in prior coursework and has a good command of the mathematical foundations of statistical theory.

In consultation with Committee faculty and Senior Instructional Professor, a doctoral student with a particularly strong mathematics and statistics background may alternatively take BUS 41901: Probability and Statistics and BUS 41902: Inference in Econometrics and Statistics in a sequence to satisfy the course requirement in statistical theory. This sequence of Ph.D.-level courses provides a thorough introduction to Classical and Bayesian statistical theory. The two-quarter sequence provides the necessary probability and statistical background for many of the advanced courses in the Chicago Booth curriculum.

SOSC 26006/36006: Foundations for Statistical Theory. This course is designed for graduate and advanced undergraduate students who aim to develop conceptual understanding of the fundamentals of statistical theory underlying a wide array of quantitative research methods. The course introduces students to probability and statistical theory and emphasizes the connection between statistical theory and the routine practice of statistical applications in quantitative research. Students will gain basic understanding of the concepts of joint, marginal, and conditional probability, Bayes rule, probability distributions of random variables, principles of statistical inference, sampling distributions, and estimation strategies. The course can serve as a preparation for mathematical statistics courses such as STAT 244 (Statistical Theory and Methods 1) and as a theoretical foundation for various advanced quantitative methods courses in the social, behavioral, and health sciences. Prerequisite: Basic knowledge of linear algebra and calculus, specifically differentiation and integration, is necessary to understand the material on continuous distributions, multivariate distributions and functions of random variables.

STAT 24400: Statistical Theory and Methods I. This course is the first quarter of a two-quarter systematic introduction to the principles and techniques of statistics, as well as to practical considerations in the analysis of data, with emphasis on the analysis of experimental data. This course covers tools from probability and the elements of statistical theory. Topics include the definitions of probability and random variables, binomial and other discrete probability distributions, normal and other continuous probability distributions, joint probability distributions and the transformation of random variables, principles of inference (including Bayesian inference), maximum likelihood estimation, hypothesis testing and confidence intervals, likelihood ratio tests, multinomial distributions, and chi-square tests. Examples are drawn from the social, physical, and biological sciences. The coverage of topics in probability is limited and brief, so students who have taken a course in probability find reinforcement rather than redundancy.

STAT 24500: Statistical Theory and Methods II. This course is the second quarter of a two-quarter systematic introduction to the principles and techniques of statistics, as well as to practical considerations in the analysis of data, with emphasis on the analysis of experimental data. This course continues from STAT 24400 and covers statistical methodology, including the analysis of variance, regression, correlation, and some multivariate analysis. Some principles of data analysis are introduced, and an attempt is made to present the analysis of variance and regression in a unified framework. Statistical software is used.

BUS 41901: Probability and Statistics. The central topics of BUS 41901 are probability, martingales and stochastic processes. Basic concepts in probability are also covered. Prerequisites: One year of calculus. The text for the course is DeGroot and Schervish, Probability and Statistics. BUSN 41901 is cross-listed as STAT 32400.

BUS 41902: Inference in Econometrics and Statistics. The focus of this course is methods to draw inferences in econometric models. The course covers linear regression models, generalized methods of moments, nonlinear models, and time series models. The majority of the discussion covers frequentist methods focusing on the use of approximations to finite-sample sampling distributions as a means for obtaining inference. It covers methods that are appropriate for independent data as well as dependent data. We will discuss intuition for how and when to use the econometric tools developed in the class in addition to deriving some of the relevant theoretical properties. Three recommended texts are Econometrics by Hayashi, Econometric Analysis of Cross Section and Panel Data by Wooldridge, and Time Series Analysis by Hamilton. Asymptotic Theory for Econometricians (revised edition) by White provides a useful and concise reference on asymptotic results. BUSN 41901 is cross-listed as STAT 32900.