Dependent mixture models: Clustering and borrowing information

Most of the Bayesian nonparametric models for non-exchangeable data that are used in applications are based on some extension to the multivariate setting of the Dirichlet process, the best known being MacEachern's dependent Dirichlet process. A comparison of two recently introduced classes of vectors of dependent nonparametric priors, based on the Dirichlet and the normalized σ-stable processes respectively, is provided. These priors are used to define dependent hierarchical mixture models whose distributional properties are investigated. Furthermore, their inferential performance is examined through an extensive simulation study. The models exhibit different features, especially in terms of the clustering behavior and the borrowing of information across studies. Compared to popular Dirichlet process based models, mixtures of dependent normalized σ-stable processes turn out to be a valid choice being capable of more effectively detecting the clustering structure featured by the data.