Finite-dimensional Discrete Random Structures and Bayesian Clustering

Discrete random probability measures stand out as effective tools for Bayesian clustering. The investigation in the area has been very lively, with a strong emphasis on nonparametric procedures based either Dirichlet process or more flexible generalizations, such normalized independent increments (NRMI). literature finite-dimensional discrete priors is much limited and mostly confined to standard Dirichlet-multinomial model. While specification may be attractive due conjugacy, it suffers from considerable limitations when comes addressing clustering problems. In order overcome these, we introduce novel class of that arise hierarchical compositions structures. Despite analytical hurdles construction entails, are able characterize induced partition determine explicit expressions associated urn scheme posterior distribution. A detailed comparison (infinite-dimensional) NRMIs also provided: indeed, informative bounds discrepancy between laws obtained. Finally, performance our proposal over existing methods assessed real application where study publicly available dataset Italian education system comprising scores mandatory nationwide test.