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Convergence Analysis of Block Gibbs Samplers for Bayesian Linear Mixed Models with p> N (2015)
BibTeX
@MISC{Abrahamsen15convergenceanalysis,
author = {Tavis Abrahamsen and James P. Hobert},
title = {Convergence Analysis of Block Gibbs Samplers for Bayesian Linear Mixed Models with p> N},
year = {2015}
}
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Abstract
Exploration of the intractable posterior distributions associated with Bayesian versions of the general linear mixed model is often performed using Markov chain Monte Carlo. In partic-ular, if a conditionally conjugate prior is used, then there is a simple two-block Gibbs sampler available. Roman & Hobert (2015) showed that, when the priors are proper and the X matrix has full column rank, the Markov chains underlying these Gibbs samplers are nearly always geometrically ergodic. In this paper, Roman & Hobert’s (2015) result is extended by allowing improper priors on the variance components, and, more importantly, by removing all assump-tions on the X matrix. So, not only is X allowed to be (column) rank deficient, which provides additional flexibility in parameterizing the fixed effects, it is also allowed to have more columns than rows, which is necessary in the increasingly important situation where p> N. The full rank assumption on X is at the heart of Roman & Hobert’s (2015) proof. Consequently, the extension to unrestricted X requires a substantially different analysis. Key words and phrases. Conditionally conjugate prior; Convergence rate; Geometric drift condition; Markov chain;
Keyphrases
bayesian linear mixed model roman hobert block gibbs sampler convergence analysis markov chain important situation full column rank convergence rate intractable posterior distribution bayesian version fixed effect gibbs sampler full rank assumption different analysis conjugate prior geometric drift condition variance component improper prior general linear mixed model simple two-block gibbs sampler markov chain monte carlo key word rank deficient additional flexibility
