Bayesian Analysis

Bayesian inference for shape mixtures of skewed distributions, with application to regression analysis

Reinaldo B. Arellano-Valle, Luis M. Castro, Marc G. Genton, and Héctor W. Gómez

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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.

Article information

Source
Bayesian Anal. Volume 3, Number 3 (2008), 513-539.

Dates
First available in Project Euclid: 22 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1340370436

Digital Object Identifier
doi:10.1214/08-BA320

Mathematical Reviews number (MathSciNet)
MR2434401

Zentralblatt MATH identifier
1330.62242

Keywords
Posterior analysis regression model shape parameter skewness skew-normal distribution symmetry

Citation

Arellano-Valle, Reinaldo B.; Castro, Luis M.; Genton, Marc G.; Gómez, Héctor W. Bayesian inference for shape mixtures of skewed distributions, with application to regression analysis. Bayesian Anal. 3 (2008), no. 3, 513--539. doi:10.1214/08-BA320. https://projecteuclid.org/euclid.ba/1340370436


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