Bayesian Analysis of Variance Component Models via Rejection Sampling

Russell D. Wolfinger and Robert E. Kass


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.

Keywords: Jeffreys's prior, Mixed model, Posterior simulation, Reference prior, REML.

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