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Regeneration in Markov Chain Samplers

Per Mykland, Luke Tierney and Bin Yu
Journal of the American Statistical Association
Vol. 90, No. 429 (Mar., 1995), pp. 233-241
DOI: 10.2307/2291148
Stable URL: http://www.jstor.org/stable/2291148
Page Count: 9
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Regeneration in Markov Chain Samplers
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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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