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.
Publié le : 2004-04-14
Classification:
Block Gibbs sampler,
burn-in,
convergence rate,
drift condition,
geometric ergodicity,
Markov chain,
minorization condition,
Monte Carlo,
total variation distance,
60J10,
62F15
@article{1083178947,
author = {Jones, Galin L. and Hobert, James P.},
title = {Sufficient burn-in for Gibbs samplers for a hierarchical random effects model},
journal = {Ann. Statist.},
volume = {32},
number = {1},
year = {2004},
pages = { 784-817},
language = {en},
url = {http://dml.mathdoc.fr/item/1083178947}
}
Jones, Galin L.; Hobert, James P. Sufficient burn-in for Gibbs samplers for a hierarchical random effects model. Ann. Statist., Tome 32 (2004) no. 1, pp. 784-817. http://gdmltest.u-ga.fr/item/1083178947/