The Wasserstein Impact Measure (WIM): A practical tool for quantifying prior impact in Bayesian statistics

The prior distribution is a crucial building block in Bayesian analysis, and its choice will impact the subsequent inference. It is therefore important to have a convenient way to quantify this impact, as such a measure of prior impact will help to choose between two or more priors in a given situation. To this end a new approach, the Wasserstein Impact Measure (WIM), is introduced. In three simulated scenarios, the WIM is compared to two competitor prior impact measures from the literature, and its versatility is illustrated via two real datasets.