PRIN Grant 2022CLTYP4 (2023-2025) “Discrete random structures for Bayesian learning and prediction"

ABSTRACT 

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 tool for modeling heterogeneous data that may in turn live in highdimensional
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.