Exact Bayesian inference for diffusion driven Cox processes

TL;DR

This paper introduces an exact Bayesian inference method for diffusion-driven Cox processes using MCMC and retrospective sampling, avoiding discretization errors and applicable to real data.

Contribution

It presents a novel, exact MCMC-based Bayesian inference approach for Cox processes driven by diffusions, overcoming previous discretization limitations.

Findings

Method is effective in simulated examples

Applicable to real-world data analysis

No discretization error involved

Abstract

In this paper, we present a novel methodology to perform Bayesian inference for Cox processes in which the intensity function is driven by a diffusion process. The novelty lies in the fact that no discretization error is involved, despite the non-tractability of both the likelihood function and the transition density of the diffusion. The methodology is based on an MCMC algorithm and its exactness is built on retrospective sampling techniques. The efficiency of the methodology is investigated in some simulated examples and its applicability is illustrated in some real data analyzes.