A double Metropolis-Hastings sampler for spatial models with intractable normalizing constants

The problem of simulating from distributions with intractable normalizing constants has received much attention in recent literature. In this article, we propose an asymptotic algorithm, the so-called double Metropolis-Hastings (MH) sampler, for tackling this problem. Unlike other auxiliary variable algorithms, the double MH sampler removes the need for exact sampling, the auxiliary variables being generated using MH kernels, and thus can be applied to a wide range of problems for which exact sampling is not available. For the problems for which exact sampling is available, it can typically produce the same accurate results as the exchange algorithm, but using much less CPU time. The new method is illustrated by various spatial models.