  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 us to choose between two or more priors in a given situation.
A recently proposed approach consists in determining the Wasserstein distance
between posteriors resulting from two distinct priors, revealing how close or
distant they are. In particular, if one prior is the uniform/flat prior, this
distance leads to a genuine measure of prior impact for the other prior. While
highly appealing and successful from a theoretical viewpoint, this proposal
suffers from practical limitations: it requires prior distributions to be
nested, posterior distributions should not be of a too complex form, in most
considered settings the exact distance was not computed but sharp upper and
lower bounds were proposed, and the proposal so far is restricted to scalar
parameter settings. In this paper, we overcome all these limitations by
introducing a practical version of this theoretical approach, namely the
Wasserstein Impact Measure (WIM). In three simulated scenarios, we will compare
the WIM to the theoretical Wasserstein approach, as well as to two competitor
prior impact measures from the literature. We finally illustrate the
versatility of the WIM by applying it on two datasets.
