Bayesian Computation for Log-Gaussian Cox Processes--A Comparative Analysis of Methods

TL;DR

This paper compares Bayesian methods for fitting Log-Gaussian Cox Processes, evaluating their statistical and computational efficiency through simulations and real data applications in ecology and neuroimaging.

Contribution

It provides a comprehensive comparison of Hamiltonian Monte Carlo, INLA, and Variational Bayes for Log-Gaussian Cox Process modeling.

Findings

Hamiltonian Monte Carlo offers high accuracy but is computationally intensive.

INLA provides a good balance between speed and accuracy.

Variational Bayes is faster but less precise.

Abstract

The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point patterns. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Different methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulations studies as well as through applications examining both ecological data and neuroimaging data.