Bayesian inference under differential privacy

Bayesian inference is an important technique throughout statistics. The essence of Beyesian inference is to derive the posterior belief updated from prior belief by the learned information, which is a set of differentially private answers under differential privacy. Although Bayesian inference can be used in a variety of applications, it becomes theoretically hard to solve when the number of differentially private answers is large. To facilitate Bayesian inference under differential privacy, this paper proposes a systematic mechanism. The key step of the mechanism is the implementation of Bayesian updating with the best linear unbiased estimator derived by Gauss-Markov theorem. In addition, we also apply the proposed inference mechanism into an online queryanswering system, the novelty of which is that the utility for users is guaranteed by Bayesian inference in the form of credible interval and confidence level. Theoretical and experimental analysis are shown to demonstrate the efficiency and effectiveness of both inference mechanism and online query-answering system.