Statistics Seminar: "Assessment of Multiple-Chain Importance Sampling Estimators"

Aixin Tan, University of Iowa

Abstract: In Bayesian data analysis, there is often the need to compare many different possible models and priors. If the data are highly informative for the model parameters, the choice of prior will have small effects on the posterior. Otherwise, if the data only provide indirect information of the parameters of interest, priors have to be chosen with care according to certain criteria, say, based on the Bayes Factor.

It is a challenging computing problem to calculate various posterior quantities and Bayes Factors among the different Bayesian models. In this talk, we consider an importance sampling (IS) technique that efficiently combines Markov chain Monte Carlo (MCMC) samples from multiple posterior distributions. An important yet difficult problem for general MCMC estimators is assessing their standard errors. Such assessment is even more challenging for estimators that are constructed with multiple Markov chains. We provide an easy-to-implement tool to evaluate the standard errors of the multiple-chain IS estimators.

The multiple-chain IS technique will be illustrated with two data analysis problems. One in Bayesian variable selection, the other in Bayesian spatial modeling.

 

Host: Todd Kuffner