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

Jesper Møller, A. N. Pettitt, R. Reeves, Kasper Klitgaard Berthelsen

Research output: Contribution to journalJournal articleResearchpeer-review

160 Citations (Scopus)

Abstract

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.
Original languageEnglish
JournalBiometrika
Volume93
Issue number2
Pages (from-to)451-458
Number of pages8
ISSN0006-3444
Publication statusPublished - 2006

Fingerprint

Normalizing Constant
Monte Carlo Method
Ising model
Markov Chains
Monte Carlo method
Markov Chain Monte Carlo Methods
Parameter estimation
Markov processes
Maximum likelihood
Monte Carlo methods
Sampling
Metropolis-Hastings
sampling
Auxiliary Variables
Cancel
Posterior distribution
Probability Density
Maximum Likelihood Estimation
Ising Model
Parameter Estimation

Cite this

Møller, Jesper ; Pettitt, A. N. ; Reeves, R. ; Berthelsen, Kasper Klitgaard. / An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants. In: Biometrika. 2006 ; Vol. 93, No. 2. pp. 451-458.
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Møller, J, Pettitt, AN, Reeves, R & Berthelsen, KK 2006, 'An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants' Biometrika, vol. 93, no. 2, pp. 451-458.

An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants. / Møller, Jesper; Pettitt, A. N.; Reeves, R.; Berthelsen, Kasper Klitgaard.

In: Biometrika, Vol. 93, No. 2, 2006, p. 451-458.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants

AU - Møller, Jesper

AU - Pettitt, A. N.

AU - Reeves, R.

AU - Berthelsen, Kasper Klitgaard

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

M3 - Journal article

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SP - 451

EP - 458

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 2

ER -