Regeneration in Markov Chain Samplers

by Per Mykland, Luke Tierney and Bin Yu
Technical Report No. 585
School of Statistics
University of Minnesota
March 15, 1994

Mykland: Department of Statistics, Univeristy of Chicago. Research supported in part by grant DMS-8902667 and DMS-9204504 from the National Science Foundation.
Tierney: School of Statistics, University of Minnesota. Research is supported in part by grant DMS-9005858 from the National Science Foundation.
Yu: Department of Statistics, Univeristy of Wisconsin-Madison. Research supported in part by grant DAAL03-91-G-007 from the Army Research Office.

Abstract

Markov chain sampling has recently received considerable attention in the recent literature, particular in the context of Bayesian computation and maximum likelihood estimation. This paper discusses the use of Markov chain splitting, originally developed as a tool 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 also provide a useful diagnostic of the performance of the samplers. The general approach is applied to several different samplers and is illustrated in a number of examples.

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