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

• 成果类型: Article
• 署名作者: Jones, GL; Hobert, JP
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; State University System of Florida; University of Florida
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2004
• 页码: 784-817
• 关键词: chain monte-carlo; convergence-rates; data augmentation; posterior distributions; geometric ergodicity; markov-chains; diagnostics; inference

摘要

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.