Bayesian estimation of finite mixtures of univariate and multivariate skew-normal and skew-t distributions

Beschreibung

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.

Zeitraum	19 Juni 2008 → 21 Juni 2008
Ereignistitel	First Workshop of the ERCIM Working Group on Computing and Statistics
Veranstaltungstyp	Keine Angaben
Bekanntheitsgrad	International