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An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants

Moller, Jesper, Pettitt, Anthony N., Reeves, Robert W., & Berthelsen, Kasper K. (2006) An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants. Biometrika, 93(2), pp. 451-458.

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Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value. The proposal distribution is constructed so that the normalising constant cancels from the Metropolis-Hastings ratio. The method is illustrated by producing posterior samples for parameters of the Ising model given a particular lattice realisation.

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78 citations in Scopus
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63 citations in Web of Science®

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256 since deposited on 18 Jun 2007
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ID Code: 7869
Item Type: Journal Article
Keywords: Auxiliary variable method, Ising model, Markov chain Monte Carlo, Metropolis, Hastings algorithm, Normalising constant, Partition function
DOI: 10.1093/biomet/93.2.451
ISSN: 0006-3444
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Statistical Theory (010405)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2006 Oxford University Press
Copyright Statement: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version Moller, J. and Pettitt, A. N. and Reeves, R. and Berthelsen, K. K. (2006) An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants. Biometrika 93(2):pp. 451-458 is available online at: http://dx.doi.org/10.1093/biomet/93.2.451
Deposited On: 18 Jun 2007
Last Modified: 29 Feb 2012 13:22

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