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.

翻译：在本文中,我们提出了一个新方法,用于对由扩散过程驱动的强度函数的考克斯过程进行贝叶斯式推论,其中的强度函数是由扩散过程驱动的。新颖之处在于,尽管可能性函数和扩散的过渡密度都不可忽略,但没有涉及离散错误。该方法以MCMC算法为基础,其精确性以追溯性取样技术为基础。方法的效率在一些模拟实例中进行了调查,并在一些真实的数据分析中说明了其适用性。