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：差分隐私已成为在利用保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，因为它有效规避了P值的关键批评，即缺乏可解释性以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，该框架在原则性的数据生成机制下自然产生，内在地保持了所得推论的可解释性。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，我们避免了对完整数据生成机制进行建模的需求，并确保了显著的计算优势。我们还提供了一组充分条件，以在所提出框架下建立贝叶斯因子一致性结果。通过若干数值实验展示了所设计技术的实用性。