Exact Bayesian Inference for Diffusion-Driven Cox Processes

Flávio B. Gonçalves, Krzysztof G. Łatuszyński and Gareth O. Roberts

Journal of the American Statistical Association, 2024, vol. 119, issue 547, 1882-1894

Abstract: In this article, 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. Supplementary materials for this article are available online.

Date: 2024
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DOI: 10.1080/01621459.2023.2223791

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