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

Galin L. Jones, James P. Hubert

Research output: Contribution to journalArticlepeer-review

57 Scopus citations

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. hese 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.

Original languageEnglish (US)
Pages (from-to)784-817
Number of pages34
JournalAnnals of Statistics
Volume32
Issue number2
DOIs
StatePublished - Apr 2004

Keywords

  • Block Gibbs sampler
  • Burn-in
  • Convergence rate
  • Drift condition
  • Geometric ergodicity
  • Markov chain
  • Minorization condition
  • Monte Carlo
  • Total variation distance

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