A New Bound for Privacy Loss from Bayesian Posterior Sampling

Differential privacy (DP) is a state-of-the-art concept that formalizes privacy guarantees. We derive a new bound for the privacy loss from releasing Bayesian posterior samples in the setting of DP. The new bound is tighter than the existing bounds for common Bayesian models and is also consistent with the likelihood principle. We apply the privacy loss quantified by the new bound to release differentially private synthetic data from Bayesian models in several experiments and show the improved utility of the synthetic data compared to those generated from explicitly designed randomization mechanisms that privatize posterior distributions.