Title: The semi-hierarchical Dirichlet process and its application to clustering homogeneous distributions
Authors: Alessandra Guglielmi - Politecnico di Milano (Italy) [presenting]
Mario Beraha - Politecnico di Milano, Università di Bologna (Italy)
Fernando Quintana - Pontificia Universidad Catolica de Chile (Chile)
Abstract: Assessing homogeneity of distributions is an old problem that has received considerable attention, especially in the nonparametric Bayesian literature. To this effect, we propose the semi-hierarchical Dirichlet process, a novel hierarchical prior that extends a previous hierarchical Dirichlet process and that avoids the degeneracy issues of nested processes recently described. We go beyond the simple yes/no answer to the homogeneity question and embed the proposed prior in a random partition model; this procedure allows us to give a more comprehensive response to the above question and in fact find groups of populations that are internally homogeneous when such populations (two or more) are considered. Simulation studies and an application to educational data are also discussed.