Geometric Ergodicity of Gibbs and Block Gibbs Samplers for a Hierarchical Random Effects Model

James P. Hobert, Charles J. Geyer

Research output: Contribution to journalArticle

42 Scopus citations

Abstract

We consider fixed scan Gibbs and block Gibbs samplers for a Bayesian hierarchical random effects model with proper conjugate priors. A drift condition given in Meyn and Tweedie (1993, Chapter 15) is used to show that these Markov chains are geometrically ergodic. Showing that a Gibbs sampler is geometrically ergodic is the first step toward establishing central limit theorems, which can be used to approximate the error associated with Monte Carlo estimates of posterior quantities of interest. Thus, our results will be of practical interest to researchers using these Gibbs samplers for Bayesian data analysis.

Original languageEnglish (US)
Pages (from-to)414-430
Number of pages17
JournalJournal of Multivariate Analysis
Volume67
Issue number2
DOIs
StatePublished - Nov 1 1998

Keywords

  • Bayesian model, central limit theorem; drift condition; Markov chain; Monte Carlo; rate of convergence; variance components

Fingerprint Dive into the research topics of 'Geometric Ergodicity of Gibbs and Block Gibbs Samplers for a Hierarchical Random Effects Model'. Together they form a unique fingerprint.

  • Cite this