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Abstract:
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The substantial development of Bayesian inference over recent decades has owed much to the development of Markov Chain Monte Carlo algorithms, for which the Gibbs sampler has played a pivotal role. The Gibbs sampler has been popular for Bayesian treatment of linear small area estimation models, such as the Fay-Herriot model, for which it seems to be a natural fit. Relatively little attention seems to have been paid, however, to how well the Gibbs sampler performs for such models. We will examine the Gibbs sampler for Fay-Herriot models and show via numerical illustrations that its performance can be quite poor, and that much better alternatives are readily available.
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