2024/06/10 by Jordan Awan, Awan, Jordan, Andrés F. Barrientos +3 · 1 citation
Decision Sciences · Mathematics · Medicine · #Advanced Statistical Process Monitoring #Computation (stat.CO) #Cryptography and Security (cs.CR) #Data-Driven Disease Surveillance #FOS: Computer and information sciences #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2406.06231
openalex publication_date 2024/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop both theory and algorithms to analyze privatized data in unbounded differential privacy (DP), where even the sample size is considered a sensitive quantity that requires privacy protection. We show that the distance between the sampling distributions under unbounded DP and bounded DP goes to zero as the sample size n goes to infinity, provided that the noise used to privatize n is at an appropriate rate; we also establish that Approximate Bayesian Computation (ABC)-type posterior distributions converge under similar assumptions. We further give asymptotic results in the regime where the privacy budget for n goes to infinity, establishing similarity of sampling distributions as well as showing that the MLE in the unbounded setting converges to the bounded-DP MLE. To facilitate valid, finite-sample Bayesian inference on privatized data under unbounded DP, we propose a reversible jump MCMC algorithm which extends the data augmentation MCMC of Ju et al, (2022). We also propose a Monte Carlo EM algorithm to compute the MLE from privatized data in both bounded and unbounded DP. We apply our methodology to analyze a linear regression model as well as a 2019 American Time Use Survey Microdata File which we model using a Dirichlet distribution.