Bayesian Inference for Estimating Subset Proportions using Differentially Private Counts

Abstract

Abstract Recently, several organizations have considered using differentially private algorithms for disclosure limitation when releasing count data. The typical approach is to add random noise to the counts sampled from, for example, a Laplace distribution or symmetric geometric distribution. One advantage of this approach, at least for some differentially private algorithms, is that analysts know the noise distribution and hence have the opportunity to account for it when making inferences about the true counts. In this article, we present Bayesian inference procedures to estimate the posterior distribution of a subset proportion, that is, a ratio of two counts, given the released values. We illustrate the methods under several scenarios, including when the released counts come from surveys or censuses. Using simulations, we show that the Bayesian procedures can result in accurate inferences with close to nominal coverage rates.