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Journal of the American Statistical Association Volume 90, 1995 - Issue 429
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Theory and Method

Regeneration in Markov Chain Samplers

Per Mykland Department of Statistics, University of Chicago, IL, 60637
,
Luke Tierney School of Statistics, University of Minnesota, MN, 55455
&
Bin Yu University of California, Berkeley, CA, 94720
Pages 233-241 | Received 01 Nov 1992, Published online: 27 Feb 2012
 
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Abstract

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.

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