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Given a prior probability density $p$ on a compact set $K$ we characterizethe probability distribution $q_{\delta}^*$ on $K$ contained in a Wassersteinball $B_{\delta}(\mu)$ centered in a given discrete measure $\mu$ for which therelative-entropy $H(q,p)$ achieves its minimum. This characterization gives usan algorithm for computing such distributions efficiently

Minimum cross-entropy distributions on Wasserstein balls and their applications