Final Report Summary - N-BNP (New directions in Bayesian Nonparametrics)
This research project focused on statistical inference in a Bayesian nonparametric framework. Among the inferential approaches, Bayesian Nonparametrics stands out for the rich and flexible probabilistic modeling and for naturally allowing accurate function estimation via posterior distributions, which effectively exploit the information conveyed by the observed data. The main goal of the project was the introduction and investigation of innovative Bayesian nonparametric inferential methodologies and procedures.
The most notable results are the proposal and the thorough analysis of relevant distributional properties of novel nonparametric prior distributions suitable for modeling several types of dependence structures among the data. In particular, the key achievements are the derivation of analytic expressions for the partition structures and the corresponding prediction rules induced by dependent nonparametric priors, the analysis of their asymptotic and distributional properties, the investigation of their inferential implications in temporal frameworks and the elaboration of efficient and scalable computational algorithms that are used to approximate Bayesian inferences of interest. These new methodologies were successfully implemented in several applied problems arising in Genomics, Biology, Ecology, Survival Analysis and Economics. The results obtained within the project also opened up an array of novel research perspectives in Bayesian Nonparametrics and beyond, that will inspire future research.
The most notable results are the proposal and the thorough analysis of relevant distributional properties of novel nonparametric prior distributions suitable for modeling several types of dependence structures among the data. In particular, the key achievements are the derivation of analytic expressions for the partition structures and the corresponding prediction rules induced by dependent nonparametric priors, the analysis of their asymptotic and distributional properties, the investigation of their inferential implications in temporal frameworks and the elaboration of efficient and scalable computational algorithms that are used to approximate Bayesian inferences of interest. These new methodologies were successfully implemented in several applied problems arising in Genomics, Biology, Ecology, Survival Analysis and Economics. The results obtained within the project also opened up an array of novel research perspectives in Bayesian Nonparametrics and beyond, that will inspire future research.