Bayesian nonparametric location–scale–shape mixtures
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Discrete mixture models are one of the most successful approaches for density estimation. Under a Bayesian nonparametric framework, Dirichlet process location–scale mixture of Gaussian kernels is the golden standard, both having nice theoretical properties and computational tractability. In this paper we explore the use of the skew-normal kernel, which can naturally accommodate several degrees of skewness by the use of a third parameter. The choice of this kernel function allows us to formulate nonparametric location–scale–shape mixture prior with desirable theoretical properties and good performance in different applications. Efficient Gibbs sampling algorithms are also discussed and the performance of the methods are tested through simulations and applications to galaxy velocity and fertility data. Extensions to accommodate discrete data are also discussed.
KeywordsDiscrete random probability measures Model-based clustering Skew-normal distribution Rounded mixture priors
Mathematics Subject Classification62F15 62E15
The authors thank Adelchi Azzalini for his shepherding into the skew world and Pierpaolo De Blasi, Stefano Mazzucco, and Igor Prünster for comments on early versions of the paper. The comments of two anonymous referees and of the Associate Editor are gratefully acknowledged.
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