  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.
