Exact Bayesian Inference in Spatiotemporal Cox Processes Driven by Multivariate Gaussian Processes
提出一种新的推断方法，用于对强度函数依赖多元高斯过程的时空Cox过程进行贝叶斯推断，该方法无离散化误差，基于MCMC算法从参数和潜变量的联合后验分布中采样。
Summary 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 enable evolution of the intensity function over discrete time. The novelty of the method lies on the fact that no discretization 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. A particular choice of the dominating measure to obtain the likelihood function is shown to be crucial to devise a valid Markov chain Monte Carlo algorithm. The models are defined in a general and flexible way but they are amenable to direct sampling from the relevant distributions because of careful characterization of its components. The models also enable 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.