Sufficient burn-in for Gibbs samplers for a hierarchical random effects model
Statistics Theory
2007-06-13 v1 Statistics Theory
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.
Keywords
Cite
@article{arxiv.math/0406454,
title = {Sufficient burn-in for Gibbs samplers for a hierarchical random effects model},
author = {Galin L. Jones and James P. Hobert},
journal= {arXiv preprint arXiv:math/0406454},
year = {2007}
}