Interval Estimation for Binomial Proportions Under Differential Privacy

TL;DR

This paper evaluates various interval estimation methods for binomial proportions under differential privacy, highlighting the effectiveness of Bayesian credible intervals through simulation studies.

Contribution

It introduces and compares different differentially private interval estimation methods, emphasizing the advantages of Bayesian credible intervals.

Findings

Bayesian credible intervals perform best under privacy constraints.

Several methods provide reasonable interval estimates.

Performance varies with privacy mechanisms and parameters.

Abstract

When releasing binary proportions computed using sensitive data, several government agencies and other data stewards protect confidentiality of the underlying values by ensuring the released statistics satisfy differential privacy. Typically, this is done by adding carefully chosen noise to the sample proportion computed using the confidential data. In this article, we describe and compare methods for turning this differentially private proportion into an interval estimate for an underlying population probability. Specifically, we consider differentially private versions of the Wald and Wilson intervals, Bayesian credible intervals based on denoising the differentially private proportion, and an exact interval motivated by the Clopper-Pearson confidence interval. We examine the repeated sampling performances of the intervals using simulation studies under both the Laplace mechanism and discrete Gaussian mechanism across a range of privacy guarantees. We find that while several methods can offer reasonable performances, the Bayesian credible intervals are the most attractive.