Discrete random structures for Bayesian learning and prediction - Finanziamento dell’Unione Europea – NextGenerationEU – missione 4, componente 2, investimento 1.1.

This research proposal introduces innovative Bayesian models and methodologies for complex dependence structures possibly featuring high-dimensional or highly-structured data. This positions the project at the frontier of statistical research in the Data Science era. Although most objectives are motivated by intriguing and modern applications, our approach will not compromise on mathematical rigor and principled methodology; even the most computationally oriented contributions will be based on the envisaged formal theoretical results. The common thread unifying the research lines in the project is the proposal of finite- and infinite-dimensional prior distributions arising from the composition of discrete random structures, which is a convenient and effective tool for modeling heterogeneous data that may, in turn, take values in high-dimensional spaces. We envision our results to heavily impact and progress the research frontiers in the areas of predictive inference, filtering, mixture models, clustering and random partitions, computational algorithms, asymptotic validation and approximation of Bayesian procedures, as well as to significantly contribute to the advance of inferential methodologies for genomic, ecological, networks-related, financial, seismological and survival data.