Bayesian Analysis of Variance Component Models via
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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