Differential privacy has emerged as an significant cornerstone in the realm of scientific hypothesis testing utilizing confidential data. In reporting scientific discoveries, Bayesian tests are widely adopted since they effectively circumnavigate the key criticisms of P-values, namely, lack of interpretability and inability to quantify evidence in support of the competing hypotheses. We present a novel differentially private Bayesian hypotheses testing framework that arise naturally under a principled data generative mechanism, inherently maintaining the interpretability of the resulting inferences. Furthermore, by focusing on differentially private Bayes factors based on widely used test statistics, we circumvent the need to model the complete data generative mechanism and ensure substantial computational benefits. We also provide a set of sufficient conditions to establish results on Bayes factor consistency under the proposed framework. The utility of the devised technology is showcased via several numerical experiments.

提出一种新颖的差分隐私贝叶斯假设检验框架，基于统计学中广泛采用的检验统计量的差分隐私贝叶斯因子，不需要模拟完整的数据生成过程，保持结果推理的可解释性，并提供一组足够的条件来确立在该框架下的贝叶斯因子一致性结果，通过多个数值实验证明了该技术的实用性。

差分隐私贝叶斯检验