Relatore
Federico Camerlenghi
Research fellow - Dipartimento di Scienze Statistiche Bologna
Abstract
A large amount of literature in Bayesian nonparametrics has been developed for the exchangeable setting, which takes into account homogeneity across data. However, in a large variety of applied problems data are intrinsically heterogeneous being generated by different, tough related, experiments: in such situations partial exchangeability is a more appropriate assumption. In this spirit we propose two general classes of nonparametric priors, namely hierarchical and nested processes, which are based on suitable transformations of completely random measures. Besides, we are able to study their analytical properties in a systematic and rigorous way within the framework of partial exchangeability. More specifically we thoroughly analyze the random partition structure arising from hierarchical and nested priors, and besides we characterize the posterior distribution of these processes. In addition to providing a unified theory on the subject, the results also allow to devise useful sampling schemes and are relevant in several application areas. In particular we focus on prediction in species sampling problems, density estimation and survival analysis.
Organizzatori
Alessandra Luati
Silvia Cagnone