A0735
Title: Distances on random measures for Bayesian nonparametrics
Authors: Marta Catalano - Luiss University (Italy) [presenting]
Abstract: Random measures are a key component of many nonparametric models in Bayesian Statistics. Their infinite-dimensionality guarantees remarkable flexibility and generality but makes the investigation of theoretical and inferential properties more demanding. In this talk we underline how several of these properties can be investigated through suitable distances between the laws of the random measures. Some crucial desiderata for such distances are metrization of weak convergence, numerical estimation through samples, and tractability of analytical bounds: we achieve them by relying on optimal transport and integral probability metrics. Applications of our findings include the measurement of dependence in Bayesian nonparametric models, the definition of merging rates of opinions, and the quantification of the error in approximate posterior inference.
