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Sufficient burn-in for Gibbs samplers for a hierarchical random effects model

Galin L. Jones·James P. Hobert
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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.

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Galin L. Jones, James P. Hobert. 2004-06-23. Sufficient burn-in for Gibbs samplers for a hierarchical random effects model. https://doi.org/10.1214/009053604000000184

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