Differentially private Bayesian tests
This work addresses privacy concerns in scientific hypothesis testing for researchers handling sensitive data, representing an incremental advancement by integrating differential privacy with existing Bayesian methods.
The authors tackled the problem of conducting Bayesian hypothesis tests on confidential data while preserving privacy, by introducing a differentially private Bayesian testing framework that maintains interpretability and computational efficiency, achieving results demonstrated through numerical experiments.
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.