We describe Bayesian inference for the mean and variance of bounded data protected by differential privacy and modeled as Gaussian. Using this setting, we demonstrate that analysts can and should take the constraints imposed by the bounds into account when specifying prior distributions. Additionally, we provide theoretical and empirical results regarding what classes of default priors produce valid inference for a differentially private release in settings where substantial prior information is not available. We discuss how these results can be applied to Bayesian inference for regression with differentially private data.

翻译：本文描述了受差分隐私保护的边界数据在建模为高斯分布时，其均值与方差的贝叶斯推断方法。通过该设定，我们证明分析人员在设定先验分布时能够且应当考虑边界约束带来的限制。此外，针对缺乏充分先验信息的情形，我们从理论与实证层面探讨了哪些类别的默认先验能为差分隐私发布生成有效的推断结果。最后讨论了这些结论如何应用于差分隐私数据的贝叶斯回归推断。