Optimal Transport Distance Between Completely Random Measures with Applications in Bayesian Statistics

Abstract

Completely random measures (random measures whose evaluation on disjoint sets are independent random variables) are used in Bayesian Non Parametric (BNP) statistics to define prior distributions, allowing for a flexible modeling while keeping analytic tractability. We build a distance between such objects, based on an optimal transport distance between Lévy measures. We use this distance to define and compute key quantities in BNP statistics: an index of dependence, the measure of the impact of the prior and also merging rates of posterior laws. This is joint work with Marta Catalano, Antonio Lijoi and Igor Prünster.