Regeneration in Markov Chain Samplers

(REVISION)

by Per Mykland, Luke Tierney and Bin Yu
Technical Report No. 585 R(1)
School of Statistics
University of Minnesota
May 17, 1994

Per Mykland is Assistant Profession, Department of Statistics, Univeristy of Chicago, Chicago, IL 60637. Luke Tierney is Professor, School of Statistics, University of Minnesota, Minneapolis, MN 55455. Bin Yu is Assistant Profession, University of California, Berkeley, CA 94720. Research of Mykland was supported in part by grants DMS-8902667, DMS-9204504 and DMS-9305601 from the National Science Foundation. Research of Tierney was supported in part by grant DMS-9005858 and DMS-9303557 from the National Science Foundation. Research of Yu is supported in part by grant DAAL03-91-G-007 from the Army Research Office.

Abstract

Markov chain sampling has recently received considerable attention in particular in the context of Bayesian computation and maximum likelihood estimation. This paper 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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