Bayesian modeling with nested random partitions

Mixtures of Gaussian distributions are popular models for density estimation and clustering, and Bayesian nonparametric mixture models have proved extremely successful in a large range of applied fields.However, several issues remain delicate in the case of multivariate data. We discuss a multivariate mixture model where the prior on the latent distribution extends the popular Dirichlet process in allowing random nested partitions, while maintaining a simple predictive rule. This provides a more flexible description of the clustering structure of the data,without requiring additional computational costs if compared with Dirichlet process mixture models.