Bayesian analysis of a Gibbs hard-core point pattern model with varying repulsion range

Authors

Affiliation

Tuomas Rajala

University of Jyväskylä

Antti Penttinen

University of Jyväskylä

Abstract

A Bayesian solution is suggested for the modelling of spatial point patterns with inhomogeneous hard-core radius using Gaussian processes in the regularization. The key observation is that a straightforward use of the finite Gibbs hard-core process likelihood together with a log-Gaussian random field prior does not work without penalisation towards high local packing density. Instead, a nearest neighbour Gibbs process likelihood is used. This approach to hard-core inhomogeneity is an alternative to the transformation inhomogeneous hard-core modelling. The computations are based on recent Markovian approximation results for Gaussian fields. As an application, data on the nest locations of Sand Martin (Riparia riparia) colony1 on a vertical sand bank are analysed.

Fig 1. From the top down: Locations of Sand Martin’s nests on a sand bank as will be described in Section 4; data overlaid on a kernel smoothed intensity field; a simulation of an inhomogeneous Poisson process model overlaid on the mean posterior intensity field; simulation from the new varying range hard-core model overlaid on a mean posterior predictive intensity field.