language: en

Bayesian Analysis of Variance Component Models via Rejection Sampling

Russell D. Wolfinger
SAS Institute Inc.,
SAS Campus Drive, Cary, NC 27513, U.S.A.
and Robert E. Kass
Department of Statistics, Carnegie Mellon University
Pittsburgh, PA 15213, U.S.A.
January, 1996

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.

Some key words: Jeffreys's prior, Mixed model, Posterior simulation, Reference prior, REML.