Inferência bayesiana para modelos Poisson com priori conjugada baseada em misturas da distribuição Gama

Abstract

Bayesian inference is a statistical methodology that combines prior information about model parameters with observational data to estimate the posterior distribution of unknown parameters. One of the advantages of using conjugate priors is that the resulting posterior distribution remains within the same family of distributions as the prior, which facilitates both the calculations and the intuitive interpretation of the posterior parameters. In this study, we adopted mixtures of Gamma distributions as conjugate priors for the λ parameter of the Poisson distribution, which provides a more flexible approach capable of better adjusting to different data characteristics. The mixtures of Gamma distributions explored in this work include the generalized Lindley distribution 1 (ABOUAMMOH; ALSHANGITI; RAGAB, 2015), the generalized Lindley distribution 2 (RAMOS; LOUZADA; MOALA, 2021) and the generalized Lindley distribution 3 (ZAKERZADEH; DOLATI, 2009). These distributions are extensions of the classic Lindley distribution. To illustrate the practical application of the proposed methodology, we carried out a study with real data.