Exact Bayesian inference for Markov switching Cox processes

Abstract

Statistical modelling of point patterns is an important and common problem in several applications. An important point process, and a generalisation of the Poisson process, is the Cox process, where the intensity function is itself stochastic. We focus on Cox processes in which the intensity function is driven by a nite state space continuous-time Markov chain. We refer to these as Markov switching Cox processes (MSCP). We investigate some probabilistic properties of these processes, three new theorems for these processes are derived and we develop a Bayesian methodology to perform exact inference based on MCMC algorithms. Since the likelihood function is tractable, it facilitates the development of an exact methodology. Simulated studies are presented in order to investigate the efficiency of the methodology on the estimation of MSCP's intensity function and the parameters indexing its law. Finally, an analysis with real data is performed.