Exact Bayesian inference in spatiotemporal Cox processes driven by multivariate Gaussian processes

• 成果类型: Article
• 署名作者: Goncalves, Flavio B.; Gamerman, Dani
• 署名单位: Universidade Federal de Minas Gerais; Universidade Federal do Rio de Janeiro
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12237
• 发表日期: 2018
• 页码: 157-175
• 关键词: chain monte-carlo; simulation; models

摘要

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.