Bayesian Inference for Shape Mixtures of Skewed Distributions, with Application to Regression Analysis
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Date
2008
Journal Title
Journal ISSN
Volume Title
Publisher
INT SOC BAYESIAN ANALYSIS
Abstract
We introduce a class of shape mixtures of skewed distributions and study some of its main properties. We discuss a Bayesian interpretation and some invariance results of the proposed class. We develop a Bayesian analysis of the skew-normal, skew-generalized-normal, skew-normal-t and skew-t-normal linear regression models under some special prior specifications for the model parameters. In particular, we show that the full posterior of the skew-normal regression model parameters is proper under an arbitrary proper prior for the shape parameter and noninformative prior for the other parameters. We implement a convenient hierarchical representation in order to obtain the corresponding posterior analysis. We illustrate our approach with an application to a real dataset on characteristics of Australian male athletes.
Description
Keywords
Posterior analysis, regression model, shape parameter, skewness, skew-normal distribution, symmetry