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Activity Number: 47
Type: Invited
Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #303609
Title: Convergence Analysis of the Gibbs Sampler for Bayesian General Linear Mixed Models with Improper Priors
Author(s): James P. Hobert*+ and Jorge Carlos Roman
Companies: University of Florida and University of Florida
Address: Department of Statistics, Gainesville, FL, 32611,
Keywords: Posterior propriety ; Geometric ergodicity

A popular default prior for the general linear mixed model is an improper prior that takes a product form with a flat prior on the regression parameter, and so-called power priors on each of the variance components. I will describe a convergence rate analysis of the Gibbs samplers associated with these Bayesian models. The main result is a simple, easily-checked sufficient condition for geometric ergodicity of the Gibbs Markov chain.

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