Exact Bayesian inference for Markov switching Cox processes

• Autor(a) principal: Lívia Maria Dutra
• Data de Publicação: 2019
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/33569
• topic: Bayesian inference; Exact posterior distributions; Cox process; Continuous-time Markov chain; Estatística - Teses; Teoria bayesiana de decisão estatística; Markov, Processos de

Statistical modelling of point patterns is an important and common problem in several areas. Poisson process is the most common process used for this purpose and, in particular, its generalisation considers a stochastic intensity function. This is called a Cox process and different choices to model the dynamics of the intensity give raise to a wide range of flexible models. We present a new class of unidimensional Cox processes in which the intensity function is driven by parametric functional forms that switch among themselves according to a continuous-time Markov chain. We refer to these as Markov switching Cox processes (MSCP). Previous developments in the literature are used to develop a Bayesian methodology to perform exact inference based on MCMC algorithms. The reliability of the algorithm depends on a variety of specifications which are carefully addressed. Simulated and real studies are presented in order to investigate the efficiency and applicability of the proposed methodology.