Bayesian Analysis

This has been an excellent course. Professor Jackman keeps a brisk pace through the materials, but also gave time generously to respond to questions. — participant from the U.S.

This course provides participants with a practical introduction to Bayesian statistical modeling and inference, with a particular emphasis on applications across the social sciences. It begins with a brief discussion of how Bayesian statistical inference differs from classical or frequentist inference in the context of simple, familiar statistical procedures and models, such as the inference for proportions and regression. Following these initial considerations, the bulk of the course focuses on applied, simulation-based Bayesian inference, using the free software packages R and JAGS.

As this course presumes a basic background in statistics, participants without any prior statistical knowledge might want to consider taking another quantitative methods course instead.

Dates

This course was offered in 2015.

Instructor

Simon Jackman, Stanford University

Detailed Description

This course provides participants with a practical introduction to Bayesian statistical modeling and inference, with an emphasis on applications in the social sciences. Beginning slowly, the course discusses how Bayesian statistical inference differs from classical or frequentist inference. It examines these differences in the context of such statistical procedures and models as one- and two-sample t-tests, the analysis of a two-by-two tables, one-way ANOVA, and regression.

Following these initial considerations, the bulk of the course emphasizes applied, simulation-based Bayesian inference. It highlights how Bayesian approaches have become particularly attractive for more complex models thanks to the computing power that is available to researchers today. The course specifically focuses on a set of algorithms known as Markov chain Monte Carlo (MCMC) algorithms that allow social scientists to tackle classes of problems that used to fall in the 'too hard' basket.

The course examines how MCMC algorithms make Bayesian inference feasible, discusses their strengths and weaknesses, and explains some of the pitfalls to avoid when deploying MCMC algorithms. Some of the applications that are considered include:

Generalized linear models for binary and ordinal data
Multinomial choice models
Models for latent variables, e.g., item-response models
Cross-sectional and dynamic (i.e., change-point or structural break) classification and clustering
Dynamic latent state models, e.g., tracking of public opinion over time
Various hierarchical models that are appropriate to many forms of data in the social sciences
Predictive inference
Topic modeling for text via latent Dirichlet allocation and variational Bayesian inference

To make Bayesian analysis a truly integral part of the participants' statistical computing toolkit, the course supplements theoretical discussions with many examples and the active use of the free general purpose Bayesian analysis program JAGS and various R packages.

Prerequisites

The course presumes a working knowledge of statistics. Familiarity with probability theory and measurement models would also be helpful, but is not formally required. Participants without any prior knowledge of statistics should consider a more basic quantitative methods course.

Requirements

Participants are expected to bring a WiFi-enabled laptop computer. Access to data, temporary licenses for the course software, and installation support will be provided by the Methods School.

Core Readings

Jackman, Simon. 2009. Bayesian Analysis for the Social Sciences. Chichester: John Wiley & Sons.