Title: A measure of the impact of the prior

Abstract: The role of the prior distribution in Bayesian statistics is well-known. Especially at small sample sizes, the prior choice may well have a strong impact on subsequent inference. But how “strong”? How can we compare distinct priors for a given situation? In this talk, I will propose a measure of prior impact based on Wasserstein distance, both from a theoretical viewpoint (upper and lower bounds, obtained in parts via Stein’s Method) as well as from a practical viewpoint (computational WIM). Various examples will illustrate the working of this new measure.