Modern Bayesian nonparametric methods
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Descrizione del progetto
Bayesian Nonparametric (BNP) methods provide an extremely fertile ground for the derivation of principled solutions to real-world statistical applications, and currently represent one of the most active research areas in Statistics.
The main goal of this project is the proposal of novel BNP methodologies, driven and inspired by modern inferential problems and the challenging mathematical questions they raise, together with a thorough investigation of their properties. A major objective is to devise statistical procedures suitable to deal with complex forms of dependence, typically not covered by the classical assumption of exchangeable observations. Relying on modern stochastic processes machinery, we will develop BNP models for dealing with covariate-dependent data, heterogeneous populations and time varying phenomena of various kinds.
A thorough and rigorous analysis of the theoretical properties and methodological implications will be conducted on the new models proposed within the project and also on some of the most established BNP procedures for which relevant problems are still open in the literature. The properties to be investigated include the study of distributional characteristics, foundational aspects, asymptotic behaviour and general approximation schemes, among others. The analyses will be completed by the design of suitable sampling algorithms allowing the actual implementation of the proposed models to specific challenging applications. Together, these elements will provide concrete statistical procedures for estimation, forecasting, clustering and theoretical validation for many and diverse inferential goals. A major impact of the project's results on current BNP research is envisaged and will be favoured by extensive comparisons with current alternative methodologies.