Exact Bayesian inference for diffusion driven Cox processes

07/11/2020

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by   Flavio B. Gonçalves, et al.

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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 on the fact that no discretisation 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 analyses.