Differentially Private Bayesian Tests

Hypothesis testing is an indispensable tool to answer scientific questions in the context of clinical trials, bioinformatics, social sciences, etc. The data within such domains often involves sensitive and private information pertaining to individuals. Researchers often bear legal obligations to safeguard the privacy of such data. In this context, differential privacy (Dwork, 2006) has emerged as a compelling framework for ensuring privacy in statistical analyses with confidential data. Consequently, differentially private versions of numerous well-established hypothesis tests have been developed, although exclusively from a frequentist view point. This encompasses private adaptations of test of binomial proportions (Awan and Slavković, 2018), linear regression (Alabi and Vadhan, 2023), goodness of fit (Kwak et al., 2021), analysis of variance (Swanberg et al., 2019), high-dimensional normal means (Narayanan, 2022), to name a few. Differentially private versions of common non-parametric tests (Couch et al., 2019), permutation tests (Kim and Schrab, 2023), etc., have emerged as