Métodos de estimação de modelos de mistura para dados com Distribuição Poisson

Abstract

Mixture models are only used when population data can be partitioned into subpopulations. This methodology allows the use of multiple probability distributions, so that each one determines the behavior of each subpopulation. In this work we study mixture model estimation methods for contagion data, focusing on the Bayesian approach. Two methods are presented here: EM (expectation-maximization algorithm), MH (Metropolis-Hasting). The first mentioned is based on maximum likelihood, there is no Bayesian inference. Applications were made using the EM and MH methods, in simulated databases with even variables. The methodologies are also applied to a real database. From two results, there are possible indications that the methods will perform well when the parameters are close. These estimates are even better for distant parameters. I also verified that as the sample size increases, these estimates are smaller, or what was expected.