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Analysis of the Gibbs sampler for a model related to James-Stein estimators

✍ Scribed by Jeffrey S. Rosenthal

Publisher: Springer US
Year: 1996
Tongue: English
Weight: 604 KB
Volume: 6
Category: Article
ISSN: 0960-3174
DOI: 10.1007/bf00140871

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✦ Synopsis

We analyse a hierarchical Bayes model which is related to the usual empirical Bayes formulation of James-Stein estimators. We consider running a Gibbs sampler on this model. Using previous results about convergence rates of Markov chains, we provide rigorous, numerical, reasonable bounds on the running time of the Gibbs sampler, for a suitable range of prior distributions. We apply these results to baseball data from . For a different range of prior distributions, we prove that the Gibbs sampler will fail to converge, and use this information to prove that in this case the associated posterior distribution is non-normalizable.

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