Penalized composite likelihoods for inhomogeneous Gibbs point process models

Abstract

A novel general framework is presented for regularizing inhomogeneous Gibbs point process models via composite likelihood with convex penalty functions. Both penalized pseudolikelihood and a new approach based on penalized logistic composite likelihood are considered, and the selection properties and predictive performance of these two methods are evaluated in a simulation study. The use of composite information criteria for penalty tuning parameter selection is also investigated. A new criterion is proposed based on the extended regularized information criterion (ERIC), which outperforms other composite information criteria in simulations. In a species distribution modelling application, the new methods are compared to MAXENT, a popular software package that also fits regularized point process models. The models obtained using the new methods exhibit similar or better fit to the data than the MAXENT model while being sparser and more interpretable.