Bayesian modeling of Tuberculosis notifications using the generalized Poisson distribution

Authors

DOI:

https://doi.org/10.5902/2179460X91810

Keywords:

Bayesian inference, Hamiltonian Monte Carlo, Time series analysis, Tuberculosis

Abstract

Time series models are widely applied across various scientific areas, enabling forecasting and trend identification. Traditional approaches, such as those based on the Autoregressive Moving Average class, have been expanded in the literature, with the generalized Autoregressive Moving Average (GARMA) models being an example of this expansion, allowing the analysis of discrete, rate, or proportion time series. However, when dealing with count time series, applied studies commonly assume normality for the response or adopt distributions such as the Poisson or negative Binomial, which, in some cases, may not accommodate features such as overdispersion. In this context, this study proposes the use of the generalized Poisson and zero-adjusted generalized Poisson distributions as alternatives to these models. The models were defined using a temporal dependence structure similar to that of the GARMA model, and inference was performed through a Bayesian approach. The models were evaluated through a simulation study, and functions were developed in R, via the shiny interface, for sample generation from the zero-adjusted generalized Poisson, ensuring the reproducibility of the study. Finally, we modeled tuberculosis notifications in Minas Gerais, Brazil, providing forecasts for public health use.

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Author Biographies

Luiz Otávio de Oliveira Pala, Universidade Federal de Lavras

Possui graduação em Ciências Atuariais, mestrado em Estatística Aplicada e Biometria e doutorado em Estatística e Experimentação Agropecuária. Desenvolve pesquisas em Estatística Aplicada, com foco em modelagem de risco e de sinistros no ramo não vida, além de atuar nas áreas de séries temporais e inferência Bayesiana.

Ryan Rodrigo Oliveira de Paula, Universidade Federal de Lavras

Médico graduado pela Universidade Federal de Lavras.

Luciano José Pereira, Universidade Federal de Lavras

Professor Titular de Fisiologia Humana do Departamento de Medicina da Universidade Federal de Lavras (UFLA). Docente do Curso de Medicina, nas disciplinas de Processos Fisiológicos I, II e III. Atua como docente permanente nos Programas de Pós-Graduação em Ciências da Saúde (PPGSA/UFLA, Área Medicina II), Ciências Veterinárias (PPGCV/UFLA, Área Medicina Veterinária) e Nutrição e Saúde (PPGNS/UFLA, Área Nutrição).

Thelma Sáfadi, Universidade Federal de Lavras

Possui graduação (Licenciatura e Bacharelado) em Matematica pela Universidade Federal de Minas Gerais (1979), especialização em Matemática pela Universidade Federal de Minas Gerais, mestrado em Matemática pela Universidade Federal de Minas Gerais (1987) e doutorado em Estatística pela Universidade de São Paulo (1997). Possui pós-doutoramentos na Universidad Carlos III de Madrid (2003/2004) , na Universidade de São Paulo (2010) e na Georgia Institute of Technology (2015).

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Published

2026-07-02

Issue

Vol. 48 (2026): Publicação contínua

Section

Applied Mathematics

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