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

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)513-540
Number of pages28
JournalBayesian Analysis
Volume3
Issue number3
DOIs
StatePublished - Dec 1 2008

Keywords

  • Posterior analysis
  • Regression model
  • Shape parameter
  • Skewness
  • Skewnormal distribution
  • Symmetry

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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