Bayesian clustering: a novel nonparametric framework for borrowing strength across populations

Non-exchangeable data arise in a number of relevant applied problems and have led to the development of several statistical methodologies tailored to the type of dependence assumed among the data. Here attention is focused on the case where data originate from different studies or refer to related experiments that are performed under different conditions. In such a context, the properties of a novel flexible class of nonparametric priors are analyzed. Specifically, these priors are used to define dependent hierarchical mixture models whose features are explored, especially in terms of the clustering behavior and the borrowing of strength across studies. An extensive simulation study investigates the effect of dependence: the novel model allows for a more appropriate use of the available information and, in turn, leads to a better understanding of the clustering structure underlying the data. The degree of dependence between priors does not need to be set by the experimenter as the Bayesian approach naturally allows the data to determine it.