N-BNP - New Directions in Bayesian Nonparametrics

The popularity of Bayesian nonparametric (BNP) inference is .rapidly growing within both the academic community and practitioners. Indeed the BNP 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 BNP paradigm in the '30s, the first methodological breakthroughs in the '?Os, and major theoretical and computational progress in the following 40 years, further significant developments of BNP are nowadays needed for providing successful answers to the practical challenges of the XXI century emerging from diverse applied fields. Therefore, the main objective of the present research project is to introduce and investigate novel methodologies and procedures for BNP 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, 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, among which nonparametric regression, meta-analysis, competing risks, macroeconomic dynamics, population processes with spatial immigration and time-varying mutation rate, credit markets with heterogeneous agents, biodiversity assessment and prediction in Ecology and Genomics. 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 features of BNP.