Banca de QUALIFICAÇÃO: KARINE DOS SANTOS ARAUJO

Uma banca de QUALIFICAÇÃO de MESTRADO foi cadastrada pelo programa.
STUDENT : KARINE DOS SANTOS ARAUJO
DATE: 11/12/2024
TIME: 14:00
LOCAL: Ambiente virtual
TITLE:

Bayesian Inference for Poisson Models with Conjugate Prior Based on Gamma Mixture Distributions

KEY WORDS:

Bayesian Inference; Gamma Mixtures; Conjugate Prior; Poisson Distribution.

PAGES: 44
BIG AREA: Ciências Exatas e da Terra
AREA: Probabilidade e Estatística
SUMMARY:

Bayesian inference is a statistical methodology that combines prior information about the model parameters with observational data to estimate the posterior distribution of unknown parameters. One advantage of using conjugate priors is that the resulting posterior distribution remains within the same family as the prior distribution, which simplifies both the calculations and the intuitive interpretation of the posterior parameters. In this study, we adopt mixtures of Gamma distributions as conjugate priors, providing a more flexible approach that can better adapt to the different characteristics of the data, allowing for a more accurate estimation of the Poisson model parameter. The Gamma mixtures explored 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 and are notable for their versatility, enabling them to fit a wide variety of scenarios and data. We discuss the advantages of the proposed distributions compared to the conventional Gamma distribution, highlighting the benefits of using these mixtures as priors in Poisson data modeling. To illustrate the practical application of the proposed methodology, we conducted a study using real data.

COMMITTEE MEMBERS:
Interno - 3010614 - ELIARDO GUIMARAES DA COSTA
Interno - 1781198 - FIDEL ERNESTO CASTRO MORALES
Presidente - 1023112 - MARCELO BOURGUIGNON PEREIRA