Adaptive Markov chain Monte Carlo through regeneration


Gilks, Walter R., Roberts, Gareth O. and Sahu, Sujit K. (1998) Adaptive Markov chain Monte Carlo through regeneration. Journal of the American Statistical Association, 93, (443), 1045-1054.

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Description/Abstract

Markov chain Monte Carlo (MCMC) is used for evaluating expectations of functions of interest under a target distribution π. This is done by calculating averages over the sample path of a Markov chain having π as its stationary distribution. For computational efficiency, the Markov chain should be rapidly mixing. This sometimes can be achieved only by careful design of the transition kernel of the chain, on the basis of a detailed preliminary exploratory analysis of π, An alternative approach might be to allow the transition kernel to adapt whenever new features of π are encountered during the MCMC run. However, if such adaptation occurs infinitely often, then the stationary distribution of the chain may be disturbed. We describe a framework, based on the concept of Markov chain regeneration, which allows adaptation to occur infinitely often but does not disturb the stationary distribution of the chain or the consistency of sample path averages.

Item Type: Article
ISSNs: 0162-1459 (print)
Related URLs:
Keywords: adaptive method, bayesian inference, gibbs sampling, markov chain monte marlo, metropolis-hastings algorithm, mixing rate, regeneration, splitting
Subjects: Q Science > QA Mathematics
H Social Sciences > HA Statistics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Statistics
ePrint ID: 30027
Date Deposited: 11 May 2007
Last Modified: 27 Mar 2014 18:18
URI: http://eprints.soton.ac.uk/id/eprint/30027

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