# A general measure of the impact of priors in Bayesian statistics via Stein's Method

## TL;DR

This paper introduces a new measure based on Wasserstein distance to quantify how different prior choices affect posterior distributions in Bayesian models, demonstrated on common statistical models.

## Contribution

It proposes a general, quantifiable measure of prior impact in Bayesian analysis using Stein's Method and Wasserstein distance, applicable across various models.

## Key findings

- Effective in measuring prior influence on posteriors.
- Applicable to normal, Binomial, and Poisson models.
- Provides a unified framework for prior impact assessment.

## Abstract

We propose a measure of the impact of any two choices of prior distributions by quantifying the Wasserstein distance between the respective resulting posterior distributions at any fixed sample size. We illustrate this measure on the normal, Binomial and Poisson models.