Compositions of discrete random structures in Bayesian nonparametrics

Abstract: Compositions of discrete random probability measures are effective tools in Bayesian nonparametrics for modeling multiple sample data. Hierarchical processes are a noteworthy example, as their infinite-dimensional layers are able to capture latent features that account for data heterogeneity and allow for borrowing of information across different samples.

In this talk we consider some general families of hierarchical compositions and will highlight their relevant distributional properties, with a special focus on the data depend-ence structure they induce and on the clustering they generate within and across different samples. The presentation of the theoretical results will be complemented by some illustrative examples.