Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

Bayesian Analysis of Variance Component Models via Rejection Sampling

Publication Date

January, 1996

Publication Type

Tech Report

Author(s)

Russell D. Wolfinger and Robert E. Kass

Abstract

We consider the usual Normal linear mixed model for "components of variance" from a Bayesian viewpoint. Instead of using Gibbs sampling or other Markov Chain schemes that rely on full conditional distributions, we propose and investigate a method for simulating from posterior distributions based on rejection sampling. The method applies with arbitrary prior distributions but we also employ as a default reference prior a version of Jeffreys's prior based on the integrated ("restricted") likelihood. We demonstrate the ease of application and flexibility of this approach in several familiar settings, even in the presence of unbalanced data. A program implementing the algorithm discussed here will be available in the SAS MIXED procedure.