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.
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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|Item Type:||Journal Article|
|Keywords:||Auxiliary variable method, Ising model, Markov chain Monte Carlo, Metropolis, Hastings algorithm, Normalising constant, Partition function|
|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 23:22|
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