Lunch Seminar Mathematics & Statistics (LSE) - 2020/2021

Interviene: Marta Catalano, Università di Torino

Link: aula virtuale Teams 

Abstract 

Bayesian nonparametric models are a prominent tool to perform flexible inference and provide a natural quantification of uncertainty. The main ingredients are random structures on spaces of probability distributions, usually referred to as random probability measures. Their law acts as prior distribution for infinite-dimensional parameters in the models and, combined with the data, provides the posterior distribution. Recent works use dependent random measures to perform simultaneous inference across multiple samples. The borrowing of strength across different samples is regulated by the dependence structure of the random measures, with complete dependence corresponding to maximal share of information and fully exchangeable observations. For a substantial prior elicitation it is crucial to quantify the dependence in terms of the hyperparameters of the models. State-of-the-art methods partially achieve this through the expression of the pairwise linear correlation. In this talk we propose the first non-linear measure of dependence for random measures. Dependence is characterized in terms of distance from exchangeability through a suitable metric on vectors of random measures based on the Wasserstein distance. This intuitive definition extends naturally to an arbitrary number of samples and it is analytically tractable on noteworthy models in the literature.