JSM 2005 - Toronto

Abstract #302985

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Activity Number: 16
Type: Topic Contributed
Date/Time: Sunday, August 7, 2005 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #302985
Title: Moving Beyond Compatibility: The Future of the Gibbs Sampler?
Author(s): David A. van Dyk*+ and Xiao-Li Meng
Companies: University of California, Irvine and Harvard University
Address: Department of Statistics, Irvine, CA, 92697-1250, United States
Keywords: Gibbs Sampler ; Convergence ; Incompatible distributions ; Autocorrelation ; MCMC
Abstract:

Ensuring the compatibility in conditional distributions is commonly emphasized in the constructions of Gibbs samplers: Compatibility is a necessary condition for proper convergence. Recently, however, we have gradually realized Gibbs samplers appropriately constructed with incompatible distributions can lead to much more efficient MCMC algorithms than their compatible counterparts. By giving up proper convergence of the joint chain, we can achieve faster convergence of the marginal chains. This is a small sacrifice when some of the variables are artificially constructed (as with auxiliary variables or data augmentation) and their joint distribution with the primary variables is of little interest. As an illustration, it is easy to construct a two-step Gibbs sampler with incompatible distributions so the autocorrelation is actually negative while maintaining properly converging marginal chains. This is impossible for two-step Gibbs samplers constructed with compatible distributions. We present examples and preliminary theory to demonstrate the potential benefits of exploring incompatibility within Gibbs samplers. This is joint work with Xiao Li Meng at Harvard.

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