Bayesian Analysis of Linear Regression Models Using Exact Markov Chain Monte Carlo

Jason Phillip Bentley
University of Canterbury

Bayesian variable selection (BVS) typically requires Markov chain Monte Carlo (MCMC) exploration of large sample spaces. MCMC methods provide samples distributed approximately according to the stationary distribution of a Markov chain. Coupling from the past (CFTP) proposed by Propp and Wilson (1996), outlines a framework for exact MCMC methods. We investigate the use of an exact Gibbs sampler for BVS in linear regression models using a posterior distribution proposed by Celeux et al (2006). We consider this within the wider context of Bayesian analysis of linear regression models. We use simulated and real data studies to assess performance and inference. We consider methods proposed by Huang and Djuric (2002) and Corcoran and Schneider (2004). We find that the CFTP Gibbs sampler method provides exact samples, while the monotone version provides only close to exact samples. We conclude that exact MCMC methods for Bayesian analysis in linear regression benefit the accuracy of inference when their use is available.

Session 1b, Statistical Methodology: 13:30 — 13:50, Room 446

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