artículo
The Semi-Hierarchical Dirichlet Process and Its Application to Clustering Homogeneous Distributions
Fecha
2021Registro en:
10.1214/21-BA1278
1936-0975
1931-6690
WOS:000754390900006
Autor
Beraha, Mario
Guglielmi, Alessandra
Quintana, Fernando A.
Institución
Resumen
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 the hierarchical Dirichlet process of Teh et al. (2006) and that avoids the degeneracy issues of nested processes recently described by Camerlenghi et al. (2019a). 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 I >= 2 such populations are considered. We study theoretical properties of the semi hierarchical Dirichlet process and of the Bayes factor for the homogeneity test when I = 2. Extensive simulation studies and applications to educational data are also discussed.