Banca de QUALIFICAÇÃO: WALFRIDO SIQUEIRA CAMPOS JUNIOR

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
STUDENT : WALFRIDO SIQUEIRA CAMPOS JUNIOR
DATE: 21/08/2025
TIME: 09:30
LOCAL: meet.google.com/rcn-nbzg-chh
TITLE:

METHODS GENERATORS OF MULTIBASELINE, MULTIPARAMETRIC AND MULTIVARIATE PROBABILITY DISTRIBUTION CLASSES VIA BAYESIAN STATISTICS.

KEY WORDS:

Bayesian Statistics, Classes of Distributions, Multivariate Modeling, Multibaseline Distributions, Flexible Inference, Marshall-Olkin Copula.

PAGES: 90
BIG AREA: Ciências Exatas e da Terra
AREA: Probabilidade e Estatística
SUMMARY:

This thesis proposes a methodological, computational, and mathematical study to address an existing gap in the statistical literature concerning the construction of generating methods for multibaseline, multiparametric, and multivariate classes of probability distributions via Bayesian statistics. While methods for such construction exist in classical statistics, notably Brito's method (2014), no analogous studies have been developed using Bayesian inference. This absence limits modeling flexibility for complex and atypical phenomena, which often do not fit well with traditional probabilistic distributions or existing families of distributions, and hinders the systematic combination of prior information with observational evidence to generate joint distributions that represent complex uncertainties. The main objective of this work is to develop new classes of probability distributions capable of accommodating different types of situations and complex data, expanding the possibilities of statistical modeling. To this end, the main research question addressed is: how to develop a model for generating posterior distributions from varied combinations of marginal distributions and dependence structures, maintaining Bayesian coherence and inferential flexibility? The methodology employed is quantitative, based on the extension and adaptation of Brito's method (2014) ideas and demonstrations to the context of Bayesian inference. This process involves the rigorous derivation and analytical manipulation of probability density functions (p.d.f.) and cumulative distribution functions (c.d.f.) for the construction of classes applicable to prior, likelihood, and posterior distributions. Additionally, the study encompasses the derivation of the mathematical properties of these new classes, such as expansions for the probability distribution function and cumulative distribution function, risk function, Moment Generating Function (MGF), characteristic function, moments of orders, central moments, kurtosis, and skewness. Computationally, scripts developed in R were used, with numerical integration via cubature for calculating normalization constants and three-dimensional visualization of the distributions. Each analyzed scenario involved a specific combination of simulated data, marginal priors, and dependence structure, exploring different inferential behaviors of the posterior distribution. The main results obtained indicate that the choice of the prior and the dependence structure plays a decisive role in the form of the posterior distribution. In particular, multimodal prior distributions, such as mixtures of normals, generate posteriors with multiple peaks, even with informative data. Conversely, strongly informative and concentrated priors interact with weak data, producing posteriors with greater dispersion. The Marshall-Olkin copula proved efficient for modeling positive and asymmetric dependencies between parameters, with a direct impact on the shape of the joint density surface. Although applications to real data are planned for later stages, the study already demonstrates the importance and breadth of the method through the creation and analysis of a bibaseline, bivariate, and biparametric model. We conclude that the proposal of this thesis offers a promising path for the flexible generation of multivariate distributions under the Bayesian paradigm, with strong potential for application in problems where there are multiple sources of uncertainty. Theoretical implications include advancing the understanding of how complex priors interact with observational evidence under dependence. Practical applications span modeling in Bayesian networks, inference in complex systems, machine learning, and various other fields of knowledge, such as social sciences, health, economics, and engineering. Future research may explore extensions to higher dimensions and integrations with sampling methods like MCMC.

COMMITTEE MEMBERS:
Externo à Instituição - CICERO CARLOS RAMOS DE BRITO - IFPE
Interno - KLEBER NAPOLEAO NUNES DE OLIVEIRA BARROS
Presidente - MOACYR CUNHA FILHO
Externo ao Programa - 384195 - VICTOR CASIMIRO PISCOYA - nullInterno - WILSON ROSA DE OLIVEIRA JUNIOR