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Statistical modeling of point patterns is an important and common problem inseveral areas. The Poisson process is the most common process used for thispurpose, in particular, its generalization that considers the intensityfunction to be stochastic. This is called a Cox process and different choicesto model the dynamics of the intensity gives rise to a wide range of models. Wepresent a new class of unidimensional Cox process models in which the intensityfunction assumes parametric functional forms that switch among them accordingto a continuous-time Markov chain. A novel methodology is proposed to performexact Bayesian inference based on MCMC algorithms. The term exact refers to thefact that no discrete time approximation is used and Monte Carlo error is theonly source of inaccuracy. The reliability of the algorithms depends on avariety of specifications which are carefully addressed, resulting in acomputationally efficient (in terms of computing time) algorithm and enablingits use with large data sets. Simulated and real examples are presented toillustrate the efficiency and applicability of the proposed methodology. Aspecific model to fit epidemic curves is proposed and used to analyze data fromDengue Fever in Brazil and COVID-19 in some countries.

Exact and computationally efficient Bayesian inference for generalized Markov modulated Poisson processes