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28 March 2024
 
  » arxiv » math.ST/0406454

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Sufficient burn-in for Gibbs samplers for a hierarchical random effects model
Galin L. Jones ; James P. Hobert ;
Date 23 Jun 2004
Journal Annals of Statistics 2004, Vol. 32, No. 2, 784-817 DOI: 10.1214/009053604000000184
Subject Statistics MSC-class: 60J10 (Primary) 62F15 (Secondary) | math.ST
AbstractWe 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.
Source arXiv, math.ST/0406454
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