A toolbox for fitting complex spatial point process models using integrated nested Laplace approximation (INLA)

TL;DR

This paper introduces a computational toolbox leveraging INLA for efficiently fitting complex spatial point process models, including log-Gaussian Cox processes with local interactions, and demonstrates its effectiveness through simulations and real data applications.

Contribution

The paper develops a versatile INLA-based methodology for fitting complex spatial point process models with local interactions, enhancing speed and model assessment capabilities.

Findings

Efficient inference for complex spatial models achieved with INLA.

Method performs well in simulation studies.

Successfully applied to large rainforest data and multi-mark point patterns.

Abstract

This paper develops methodology that provides a toolbox for routinely fitting complex models to realistic spatial point pattern data. We consider models that are based on log-Gaussian Cox processes and include local interaction in these by considering constructed covariates. This enables us to use integrated nested Laplace approximation and to considerably speed up the inferential task. In addition, methods for model comparison and model assessment facilitate the modelling process. The performance of the approach is assessed in a simulation study. To demonstrate the versatility of the approach, models are fitted to two rather different examples, a large rainforest data set with covariates and a point pattern with multiple marks.