An analysis of Monte Carlo methods for likelihood estimation of Gibbsian images

A unified analysis of two Monte Carlo algorithms for estimating the likelihood function of Gibbs random field images is presented. It is shown that such an estimation reduces to estimating the partition functions of suitably chosen Gibbs random fields. The first algorithm requires drawing samples from a mutually compatible Gibbs random field and provides unbiased and consistent estimators of these partition functions. The second algorithm uses samples which are approximately drawn from the Gibbs distribution, and results in asymptotically unbiased and consistent estimators of the partition functions. A measure of the computational complexity of these algorithms which makes it possible to compare them is introduced. It is concluded that the first algorithm is superior, especially for models with strong interactions.<>