Logistic regression for spatial Gibbs point processes

Abstract

We propose a computationally efficient technique, based on logistic regression, for fittingGibbs point process models to spatial point pattern data. The score of the logistic regression is anunbiased estimating function and is closely related to the pseudolikelihood score. Implementationof our technique does not require numerical quadrature, and thus avoids a source of bias inherentin other methods. For stationary processes, we prove that the parameter estimator is stronglyconsistent and asymptotically normal, and propose a variance estimator. We demonstrate theefficiency and practicability of the method on a real dataset and in a simulation study.