Differentially Private Bayesian Tests
Abhisek Chakraborty Saptati Datta
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.