# Paul Freulon [03/05/2022]

Paul Freulon (IMB)

An Introduction to the Wasserstein distance in Statistics

In this talk, I will give an introduction to the Wasserstein distance and its use in statistics. In a first part, I will present a bio-statistical application that will motivate the need to compare probability distributions. In a second part, I will introduce the Wasserstein distance with some historical elements. For instance, I plan to talk about Monge problem formulated in 1781, Kantorovich contributions in the 1940’s, and why statisticians have currently a lot of interest for this distance. In a third part, I will present some explicit formulations of the Wasserstein distance and a few properties of this distance. Finally, I will try to give some statistical results related to this distance. For instance, given samples from two distributions $\mu$ and $\nu$ how can we estimate the Wasserstein distance between those two distributions?