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.