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.

翻译：差分隐私已成为利用机密数据进行科学假设检验领域的重要基石。在报告科学发现时，贝叶斯检验被广泛采用，因其能有效规避P值的主要批评——即可解释性不足及无法量化支持竞争假设的证据。我们提出了一种新颖的差分隐私贝叶斯假设检验框架，该框架在原则性数据生成机制下自然产生，本质上保持了所得推断的可解释性。此外，通过聚焦于基于广泛使用检验统计量的差分隐私贝叶斯因子，我们规避了对完整数据生成机制建模的需求，并确保了显著的计算优势。我们还提供了一组充分条件，以建立所提框架下贝叶斯因子一致性的相关结果。通过多项数值实验展示了所设计技术的实用性。