New directions in bayesian nonparametrics
The Collegio Carlo Alberto hosts a five-year research project funded by the European Research Council under the European Union's Seventh Framework Programme.
New directions in Bayesian Nonparametrics
Igor Prünster (University of Torino & Collegio Carlo Alberto)
Julyan Arbel (Collegio Carlo Alberto)
Pierpaolo De Blasi (University of Torino & Collegio Carlo Alberto)
Stefano Favaro (University of Torino & Collegio Carlo Alberto)
Antonio Lijoi (University of Pavia)
Matteo Ruggiero (University of Torino & Collegio Carlo Alberto)
All team members are part of the "de Castro" Statistics Initiative.
The popularity of Bayesian nonparametric inference is rapidly growing within both the academic community and practitioners. Indeed the Bayesian nonparametric viewpoint naturally allows for rich and flexible probabilistic modeling and, via conditional (or posterior) distributions, for accurate function estimation, most notably of probability distributions, regression functions and hazard rates. After de Finetti's theoretical foundation of the Bayesian nonparametric paradigm in the '30s of the previous century, the first methodological breakthroughs in the '70s, and major theoretical and computational progress in the following 40 years, further significant developments of Bayesian nonparametrics are nowadays needed for providing successful answers to the practical challenges of the XXI century emerging from diverse applied fields.
The main objective of the present research project is to introduce and investigate novel methodologies and procedures for Bayesian nonparametric inference. The advances will include the development of new types of covariate-dependent random discrete distributions in contexts of partial exchangeability, the derivation of general classes of nonparametric estimators suitable for several prediction problems, the construction of various types of dynamic particle systems and associated diffusion approximations via measure-valued processes, the frequentist asymptotic validation of the most up-to-date Bayesian procedures. The theoretical investigation will be complemented by the implementation of the obtained results in a variety of applied contexts. The modern probabilistic techniques needed to address challenging inferential issues explain the interplay between theory and applications which is a major headline of this project and represents one of the distinctive and attractive features of Bayesian nonparametrics.