Adaptive Markov chain Monte Carlo through regeneration
Adaptive Markov chain Monte Carlo through regeneration
Markov chain Monte Carlo (MCMC) is used for evaluating expectations of functions of interest under a target distribution ?. This is done by calculating averages over the sample path of a Markov chain having ? 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 ?, An alternative approach might be to allow the transition kernel to adapt whenever new features of ? 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.
adaptive method, bayesian inference, gibbs sampling, markov chain monte marlo, metropolis-hastings algorithm, mixing rate, regeneration, splitting
1045-1054
Gilks, Walter R.
45c85ba1-819a-46ac-823a-ab7c2766950e
Roberts, Gareth O.
f799af60-e7bf-4c2c-8d43-9be31c3b5d68
Sahu, Sujit K.
33f1386d-6d73-4b60-a796-d626721f72bf
1998
Gilks, Walter R.
45c85ba1-819a-46ac-823a-ab7c2766950e
Roberts, Gareth O.
f799af60-e7bf-4c2c-8d43-9be31c3b5d68
Sahu, Sujit K.
33f1386d-6d73-4b60-a796-d626721f72bf
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), .
Abstract
Markov chain Monte Carlo (MCMC) is used for evaluating expectations of functions of interest under a target distribution ?. This is done by calculating averages over the sample path of a Markov chain having ? 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 ?, An alternative approach might be to allow the transition kernel to adapt whenever new features of ? 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.
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Published date: 1998
Keywords:
adaptive method, bayesian inference, gibbs sampling, markov chain monte marlo, metropolis-hastings algorithm, mixing rate, regeneration, splitting
Organisations:
Statistics
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Local EPrints ID: 30027
URI: http://eprints.soton.ac.uk/id/eprint/30027
ISSN: 0162-1459
PURE UUID: 39882961-7b7d-47a6-8ddc-5e41bed4238a
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Date deposited: 11 May 2007
Last modified: 09 Jan 2022 03:03
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Contributors
Author:
Walter R. Gilks
Author:
Gareth O. Roberts
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