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

• 成果类型: Article
• 署名作者: Moller, J.; Pettitt, A. N.; Reeves, R.; Berthelsen, K. K.
• 署名单位: Aalborg University; Queensland University of Technology (QUT); Aalborg University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/93.2.451
• 发表日期: 2006
• 页码: 451458
• 关键词: models; likelihood; inference; ratios

摘要

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.