B1064
Title: Wasserstein bounds through Stein's method with bespoke derivatives
Authors: Yvik Swan - Universite libre de Bruxelles (Belgium) [presenting]
Abstract: Stein's method is used to propose new bounds on the Wasserstein distance $W_1(X,Z):=\int_{-\infty}^{+\infty} | \mathbb{P}[X \le z] - \mathbb{P}[Z \le z] | dz$ between the laws of real random variables $X$ and $Z$ under the assumption that $X$ is discrete and $Z$ is continuous. Our approach uses a new family of discrete Stein operators for the law of $X$ which are specifically designed for the purpose of comparing with the law of $Z$. The results are illustrated on a variety of examples, including Beta approximation for Polya-Eggenberger urn models, exponential approximation for the eigenvalues of the Bernoulli-Laplace Markov chains, normal approximations of integer-valued distribution, and several more if-time permits.
