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Sufficient burn-in for Gibbs samplers for a hierarchical random effects model. The Annals of Statistics (2004)
| Citations: | 39 - 16 self |
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@MISC{Jones04sufficientburn-in,
author = {L. Jones and James P. Hobert},
title = {Sufficient burn-in for Gibbs samplers for a hierarchical random effects model. The Annals of Statistics},
year = {2004}
}
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Abstract
We consider Gibbs and block Gibbs samplers for a Bayesian hierarchical version of the one-way random effects model. Drift and minorization conditions are established for the underlying Markov chains. The drift and minorization are used in conjunction with results from J. S. Rosenthal [J. Amer. Statist. Assoc. 90 (1995) 558– 566] and G. O. Roberts and R. L. Tweedie [Stochastic Process. Appl. 80 (1999) 211–229] to construct analytical upper bounds on the distance to stationarity. These lead to upper bounds on the amount of burn-in that is required to get the chain within a prespecified (total variation) distance of the stationary distribution. The results are illustrated with a numerical example. 1. Introduction. We
Keyphrases
gibbs sampler sufficient burn-in hierarchical random effect model tweedie stochastic process total variation numerical example minorization condition stationary distribution bayesian hierarchical version upper bound analytical upper bound underlying markov chain one-way random effect model
