American Statistical Association New York City Metropolitan Area Chapter Chapter Workshop December 17, 2009

Bayesian modeling and inference differs from classical inference in that it assumes a joint probability model for both the observed data and the unknown parameters. Bayesian inference is then made by examining the conditional distribution of the model parameters given the observed data. Therefore, we can make intuitive probabilistic statements about the unknown parameters like, “The posterior probability that the parameter is greater than zero is 0.95."

The first portion of this workshop will introduce participants to the basic concepts required for Bayesian data analysis. Topics will include the statistical model, prior and posterior distributions, Directed Acyclic-Graphs, and Bayesian inference. These topics will be illustrated using the normal and/or binomial distributions. After this general introduction, the workshop will introduce participants to the basics of Markov chain Monte Carlo (MCMC) and WinBugs. Specifically, topics will include an overview of MCMC, using WinBugs (syntax and the Doodle utility), and output analysis (monitoring convergence, point estimates, posterior variance and standard deviation, approximating credible intervals). These topics will be illustrated using the same simple examples from the first portion of the workshop.