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April 2004 Sufficient burn-in for Gibbs samplers for a hierarchical random effects model
Galin L. Jones, James P. Hobert
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Ann. Statist. 32(2): 784-817 (April 2004). DOI: 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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Galin L. Jones. James P. Hobert. "Sufficient burn-in for Gibbs samplers for a hierarchical random effects model." Ann. Statist. 32 (2) 784 - 817, April 2004.


Published: April 2004
First available in Project Euclid: 28 April 2004

zbMATH: 1048.62069
MathSciNet: MR2060178
Digital Object Identifier: 10.1214/009053604000000184

Primary: 60J10
Secondary: 62F15

Keywords: Block Gibbs sampler , Burn-in , convergence rate , drift condition , geometric ergodicity , Markov chain , minorization condition , Monte Carlo , total variation distance

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 2 • April 2004
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