Bayesian Strategies for Differential Privacy and Risk Assessment

Abstract

This thesis covers four contributions at the intersection of differential privacy and Bayesian methods. The first contribution is a Bayesian method for assessing statistical disclosure risks for count data released under zero-concentrated differential privacy in settings with a hierarchical structure. The second contribution is a framework for setting the privacy budget for differential privacy based on relationships between differential privacy and Bayesian posterior probabilities of disclosure. The third contribution is an examination of prior selection for Bayesian inference using statistics released under differential privacy. The fourth contribution is a series of results relating differential privacy to disclosure risk criteria, such as bounds on an adversary’s posterior probability, posterior-to-prior ratio, and posterior-to-prior difference