Monte Carlo dynamically weighted importance sampling for spatial models with intractable normalizing constants

Abstract

The problem of simulating from distributions with intractable normalizing constants has received much attention in the recent literature. In this paper, we propose a new MCMC algorithm, the so-called Monte Carlo dynamically weighted importance sampler, for tickling this problem. The new algorithm is illustrated with the spatial autologistic models. The novelty of our algorithm is that it allows for the use of Monte Carlo estimates in MCMC simulations, while still leaving the target distribution invariant under the criterion of dynamically weighted importance sampling. Unlike the auxiliary variable MCMC algorithms, the new algorithm removes the need of perfect sampling, and thus can be applied to a wide range of problems for which perfect sampling is not available or very expensive. The new algorithm can also be used for simulating from the incomplete posterior distribution for the missing data problem.