MCMC for doubly-intractable distributions

Iain Murray; Zoubin Ghahramani; David MacKay

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arXiv · 1206.6848

MCMC for doubly-intractable distributions

Iain Murray·Zoubin Ghahramani·David MacKay

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Abstract

Markov Chain Monte Carlo (MCMC) algorithms are routinely used to draw samples from distributions with intractable normalization constants. However, standard MCMC algorithms do not apply to doubly-intractable distributions in which there are additional parameter-dependent normalization terms; for example, the posterior over parameters of an undirected graphical model. An ingenious auxiliary-variable scheme (Moeller et al., 2004) offers a solution: exact sampling (Propp and Wilson, 1996) is used to sample from a Metropolis-Hastings proposal for which the acceptance probability is tractable. Unfortunately the acceptance probability of these expensive updates can be low. This paper provides a generalization of Moeller et al. (2004) and a new MCMC algorithm, which obtains better acceptance probabilities for the same amount of exact sampling, and removes the need to estimate model parameters before sampling begins.

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Iain Murray, Zoubin Ghahramani, David MacKay. 2012-06-27. MCMC for doubly-intractable distributions. https://arxiv.org/abs/1206.6848

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