Quotation Frühwirth-Schnatter, Sylvia. 2008. Bayesian estimation of finite mixtures of univariate and multivariate skew-normal and skew-t distributions. First Workshop of the ERCIM Working Group on Computing and Statistics, Neuchâtel, Schweiz, 19.06.-21.06. Invited Talk


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Abstract

Skewnormal and skew-t densities, both for univariate as well as multivariate data sets, have been introduced with the goal of capturing skewness and kurtosis without loosing unimodality of the fitted distribution. Very recently, finite mixtures of such densities have been introduced for the purpose of robust clustering. Rather little work has been done on efficient statistical estimation of such mixtures and in the present paper Bayesian inference is carried out. For mixtures of univariate and multivariate skewnormal densities, we develop MCMC estimation based on data augmentation and Gibbs sampling. The first step of data augmentation and the Gibbs sampler is based on the standard procedure of drawing classification using the skew components densities. To carry out parameter estimation within each component, we use a second step of data augmentation based on a stochastic representation of the uni- and the multivariate skewnormal density in terms of a random-effect models with truncated normal random effects. This allows drawing the parameters from standard density. This MCMC scheme is extended to univariate and multivariate mixtures of skew-t densities through a third step of data augmentation based on representing the t-density as scale mixtures of normals.

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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Paper presented at an academic conference or symposium
Language English
Title Bayesian estimation of finite mixtures of univariate and multivariate skew-normal and skew-t distributions
Event First Workshop of the ERCIM Working Group on Computing and Statistics
Year 2008
Date 19.06.-21.06
Country Switzerland
Location Neuchâtel
URL http://cfe-csda.org/ercim08/CFEERCIMBOA.pdf
Invited Talk Y

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Frühwirth-Schnatter, Sylvia (Details)
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Institute for Statistics and Mathematics IN (Details)
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