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

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

2004-06-23

arxiv.org/abs/math/0406454v1

Annals of Statistics 2004, Vol. 32, No. 2, 784-817

Mathematics

Statistics Theory

Scientific paper

10.1214/009053604000000184

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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