Stability of doubly-intractable distributions

04/15/2020

∙

by   Michael Habeck, et al.

∙

0

∙

share

Doubly-intractable distributions appear naturally as posterior distributions in Bayesian inference frameworks whenever the likelihood contains a normalizing function Z. Having two such functions Z and Z we provide estimates of the total variation and Wasserstein distance of the resulting posterior probability measures. As a consequence this leads to local Lipschitz continuity w.r.t. Z. In the more general framework of a random function Z we derive bounds on the expected total variation and expected Wasserstein distance. The applicability of the estimates is illustrated within the setting of two representative Monte Carlo recovery scenarios.