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

Flávio B Gonçalves; Lívia M Dutra; Roger W C Silva

doi:10.1007/s11222-021-10074-y

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

Stat Comput. 2022;32(1):14. doi: 10.1007/s11222-021-10074-y. Epub 2022 Jan 6.

Authors

Flávio B Gonçalves¹, Lívia M Dutra², Roger W C Silva¹

Affiliations

¹ Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627 - DEST, ICEx, UFMG, Belo Horizonte, Minas Gerais 31270-901 Brazil.
² Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, Brazil.

Abstract

Statistical modeling of temporal point patterns is an important problem in several areas. The Cox process, a Poisson process where the intensity function is stochastic, is a common model for such data. We present a new class of unidimensional Cox process models in which the intensity function assumes parametric functional forms that switch according to a continuous-time Markov chain. A novel methodology is introduced to perform exact (up to Monte Carlo error) Bayesian inference based on MCMC algorithms. The reliability of the algorithms depends on a variety of specifications which are carefully addressed, resulting in a computationally efficient (in terms of computing time) algorithm and enabling its use with large data sets. Simulated and real examples are presented to illustrate the efficiency and applicability of the methodology. A specific model to fit epidemic curves is proposed and used to analyze data from Dengue Fever in Brazil and COVID-19 in some countries.

Keywords: Fast computation; Metropolis-Hastings algorithm; Uniformization.