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

  1. K. K. Berthelsen3
  1. 1Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg E, Denmark. jm{at}math.aau.dk, 2School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Queensland 4001, Australia. a.pettitt{at}qut.edu.au, r.reeves{at}qut.edu.au, 3Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg E, Denmark. kkb{at}math.aau.dk

    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.

    Key words

    Received February 2004. Revised November 2005.

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