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Statistics seminar 2017: "Bayesian nonparametric inference beyond the Dirichlet process"

20/04/2017 dalle 12:00 alle 13:30

Dove Dipartimento di Scienze Statistiche "P. Fortunati" - Via Belle Arti 41 - Aula IV, 2° piano

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Antonio Lijoi - Università Bocconi

The Dirichlet process stands out as the cornerstone of Bayesian nonparametric modeling and most of its success is due to its analytical tractability. Nonetheless, there has recently been a rich and vivid literature on generalizations that provide greater flexibility, while still allowing for a straightforward implementation of Bayesian inferential procedures. The talk will briefly review classes of such priors that have also attracted considerable interest in applied fields. It will be noted that some of their relevant properties crucially rely on the specification of a diffuse base measure, which is interpreted as the prior guess at the shape of the data generating distribution. The case where the base measure may include atoms will be considered as well, since it is a more appropriate assumption in several applications. This makes the analysis more challenging, if one wishes to go beyond the Dirichlet process. Nonetheless, it is shown that one may still establish distributional results that, besides being of interest per se, lead to design MCMC algorithms useful for evaluating Bayesian inferences. The presentation will be completed by illustrations with real and simulated datasets.

Alessandra Luati