Likelihood inference for Gibbs processes in the analysis of spatial paint patterns

Several authors have proposed stochastic and non-stochastic approximations to the maximum likelihood estimate (MLE) for Gibbs point processes in model ling spatial point patterns with pairwise interactions. The approximations are necessary because of the difficulty of evaluating the normalizing const ant. In this paper, we first provide a review of methods which yield crude approximations to the MLE. We also review methods based on Markov chain Mon te Carlo techniques for which exact MLE has become feasible. We then presen t a comparative simulation study of the performance of such methods of esti mation based on two simulation techniques, the Gibbs sampler and the Metrop olis-Hastings algorithm, carried out for the Strauss model.