Exact Bayesian inference in spatio-temporal Cox processes driven by multivariate Gaussian processes

TL;DR

This paper introduces an exact Bayesian inference method for spatiotemporal Cox processes driven by multivariate Gaussian processes, avoiding discretisation errors and allowing flexible modeling of intensity functions over space and time.

Contribution

It presents a novel MCMC-based inference approach that handles infinite-dimensional Gaussian process models without discretisation errors, enabling flexible inclusion of covariates and temporal dynamics.

Findings

Method successfully applied to real and simulated data.

No discretisation error involved in the inference process.

Flexible modeling of space-time interactions in intensity functions.

Abstract

In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to allow for evolution of the intensity function over discrete time. The novelty of the method lies on the fact that no discretisation error is involved despite the non-tractability of the likelihood function and infinite dimensionality of the problem. The method is based on a Markov chain Monte Carlo algorithm that samples from the joint posterior distribution of the parameters and latent variables of the model. The models are defined in a general and flexible way but they are amenable to direct sampling from the relevant distributions, due to careful characterisation of its components. The models also allow for the inclusion of regression covariates and/or temporal components to explain the variability of the intensity function. These components may be subject to relevant interaction with space and/or time. Real and simulated examples illustrate the methodology, followed by concluding remarks.