Pseudo-likelihood Inference for Gibbs Processes with Exponential Families through Generalized Linear Models

Parameter estimation for two-dimensional point pattern data is difficult, because most of the available stochastic models have intractable likelihoods which usually depend on an unknown scaling factor. However, this problem can be bypassed using the pseudo-likelihood estimation method. Baddeley and Turner (1998) presented a numerical algorithm for computing approximated maximum pseudo-likelihood estimates for Gibbs point processes with exponential family likelihoods. We use their method and a new technique based on Voronoi polygons to evaluate the qua-drature points to present an intensive comparative simulation study which evaluates the performance of these two methods compared to the traditional approximation under varying circumstances. Two Gibbs point process models, the Strauss and saturation processes, have been used. This revised version was published online in June 2006 with corrections to the Cover Date.