MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancy

Understand

In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsistent estimates.

• To fix this issue, it has been suggested to replace the likelihood by a pseudo-likelihood, that is the exponential of a loss function enjoying suitable robustness properties.
• In this paper, we build a pseudo-likelihood based on the Maximum Mean Discrepancy, defined via an embedding of probability distributions into a reproducing kernel Hilbert space.
• We show that this MMD-Bayes posterior is consistent and robust to model misspecification.