Wasserstein consensus for Bayesian sample size determination

The sample size determination problem deals with the selection of the optimal number of subjects to be enrolled in a study in order to achieve a pre-specified inferential goal. While this problem can of course be approached from a frequentist viewpoint, often the Bayesian paradigm is preferred as it allows to blend and balance the strength of the observed empirical evidence with the available prior knowledge. In this work, we focus on the case of a ''community of priors'' representing, for example, different expert opinions. Within this setup, we are interested in selecting the smallest sample size that guarantees ''agreement'' between these, possibly conflicting, opinions, having formalized the loose idea of ''agreement'' in terms of the Wasserstein distance between posteriors stemming from different priors.