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Title: To choose or not to choose a prior Authors:  Fatemeh Ghaderinezhad - Gent university (Belgium) [presenting]
Abstract: The first challenging question in Bayesian statistics is how choosing the prior can affect the posterior distribution. How can the posteriors derived under different priors be similar as nowadays more and more data are collected? One of the newest and under development instruments to answer this question is Stein's method. This crafty method gives the lower and upper bounds to measure the distance of two posteriors derived under different priors (even improper priors), using the Wasserstein distance at fixed sample size. To this aim, we have proposed a methodology for tractable distributions with nested densities in one-dimensional settings. However, for practical purposes, the power of the Wasserstein distance idea has not at all been exploited so far. How can we quantify prior impact for any type of priors and any dimensions? To provide an answer to this question, we have introduced the Wasserstein Impact Measure (WIM) that relies on the numerical computation of the Wasserstein distances. It allows us to compare any two priors, thus making the WIM a fully usable alternative to the proposals from the literature.