Modelagem Bayesiana semi-paramétrica via misturas

• Ano de defesa: 2017
• Autor(a) principal: Nívea Bispo da Silva
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; UFMG
• Palavras-chave em Português: Misturas nitas de distribuições; Inferência bayesiana; Regressão linear; Distribuições de caudas pesadas; Teoria bayesiana de decisão estatística; Estatística; Análise multivariada
• Link de acesso: http://hdl.handle.net/1843/BUBD-AXGLFA

Statistical modeling based on nite mixture distributions is a growing research area. Due to its exibility and the advance of computational methods in the last two decades, this type of modeling has become quite attractive both from a practical and a theoretical point of view, since it allows densities with complex structures to be approximated using a simpler structure. In addition, statistical models based on nite mixtures can capture specic data properties such as multimodality, asymmetry, heavy tail and heterogeneity due to unobserved factors. Numerous studies on statistical modeling based on nite mixtures of normal distributions have been published in the literature, and many authors have shown that this type of mixture provides a simple and eective basis for estimating densities and modeling heterogeneous populations. However, in practical problems where there are outliers in the data, the normal distribution may have its estimates for mean and variance severely aected. In this sense there is a recent propagation of models based on mixtures withnon-normalcomponents where the assumed distributions for the components of the mixture are, for example, Student-t, Slash, Skew-Normal, Skew-t, among others. In this work a semi-parametric model based on nite mixtures of t distributions will be introduced. The proposed model specication considers separate structures for the modes and tail behavior, which makes density estimation more exible. In addition, the tail structure in the presented approach will be estimated without the need to estimate degree of freedom parameters, whose estimation is known to be dicult and computationally costly. An extension of the model in the linear regression context is also presented for situations where model errors have multimodality, asymmetry and heavy tails. The proposed approach is evaluated through simulation studies and applications to real data sets, where an MCMC algorithm is proposed and implemented to sample from the posterior distributions