Variational estimators for the parameters of Gibbs point process models

Abstract

This paper proposes a new estimation technique for fitting parametric Gibbs point process models to a spatial point pattern dataset. The technique is a counterpart, for spatial point processes, of the variational estimators for Markov random fields developed by Almeida and Gidas. The estimator does not require the point process density to be hereditary, so it is applicable to models which do not have a conditional intensity, including models which exhibit geometric regularity or rigidity. The disadvantage is that the intensity parameter cannot be estimated: inference is effectively conditional on the observed number of points. The new procedure is faster and more stable than existing techniques, since it does not require simulation, numerical integration or optimization with respect to the parameters.