Introduction to Applied Bayesian Statistics for Social Scientists

Instructor(s): Scott M. Lynch, Sociology

Bayesian statistics has received a growing amount of attention over the last decade in social science research, largely because of (1) the growth in the use of hierarchical modeling in social science coupled with the ease with which Bayesian modeling can handle such models, and (2) the development of Markov chain Monte Carlo (MCMC) simulation methods that have simplified parameter estimation. In this workshop, we will first review mathematical statistics and the classical approach to model construction and parameter estimation using maximum likelihood methods. Next, we will develop Bayes' Theorem and show its extension to probability distributions and modeling. Following the exposition of this theoretical material, we will spend considerable time presenting MCMC methods for parameter estimation, especially the Gibbs sampler and the random walk Metropolis algorithm. We will see how these methods can be used for a variety of models commonly used in social science research, including the OLS regression model, generalized linear models, hierarchical models, and multivariate models. The workshop will be highly-applied with an emphasis on using R and WinBugs for conducting Bayesian analysis. A key focus will be on comparing the Bayesian approach with the classical approach and showing the advantages of using the Bayesian approach in model evaluation and comparison, and inference. Familiarity with statistics at the level of multiple linear regression (as taught in most social science departments) is assumed. Familiarity with matrix algebra and the basic concepts underlying differential and integral calculus will be helpful, although we will briefly review these topics.