Variational estimators for the parameters of Gibbs point process models

TL;DR

This paper introduces a novel variational estimator for Gibbs point process models that is faster and more stable than existing methods, applicable to non-hereditary models without requiring simulation or complex optimization.

Contribution

It develops a new estimation technique for Gibbs point processes that does not rely on the hereditary property, expanding applicability and computational efficiency.

Findings

Estimator is faster and more stable than existing methods.

Applicable to models without a conditional intensity.

Inference is conditional on the observed number of points.

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.