Estimação de densidades via Misturas de distribuições "Skew"-normal por processos de Dirichlet"

Abstract

This work addresses the density estimation problem using non-parametric Bayesian approach. It is considered hierarchical mixture models where the uncertainty about the mixing measure is modeled using the Dirichlet process (for short, MDP). The main goal is to build a more exible model for density estimation. The normal mixture model via Dirichlet process (MNDP) originally proposed by Escobar and West (1995) is extended by considering mixtures of skew-normal distributions(MSNDP), say, in the rst stage of the hierarchical model, the normal distribution is replaced by the skew-normal one. As a by product, some important results related to Bayesian inference in the location-scale skew-normal family are introduced. The algorithm introduced by MacEachern and Muller (1998) to sample from the posteriors is used. Considering simulated data sets, the density estimates provided by MSNDP and MNDP are compared. The proposed model (MSNDP) provide much better estimates whenever the data sets comes from non-negative and skewed distributions as well as from mixture of them. If the data sets came from normal or symmetric distributions aswell as mixtures of them, the results provided by both models are comparable. MacEachern and Muller (1998) and Escobar and West (1995)'s algorithms were also compared using the MNDP andsimulated data sets. MacEachern and Muller (1998)'s algorithm usually provided better results. Finally, the Old Faithful Geyser data set taken from Silverman (1986) is analyzed using MSNDP and MNDP. The former model captured the data bimodality shown in the histogram.