Regeneration in Markov Chain Samplers

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].. American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journal of the American Statistical Association. Markov chain sampling has recently received considerable attention, in particular in the context of Bayesian computation and maximum likelihood estimation. This article discusses the use of Markov chain splitting, originally developed for the theoretical analysis of general state-space Markov chains, to introduce regeneration into Markov chain samplers. This allows the use of regenerative methods for analyzing the output of these samplers and can provide a useful diagnostic of sampler performance. The approach is applied to several samplers, including certain Metropolis samplers that can be used on their own or in hybrid samplers, and is illustrated in several examples.