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Protection of individual privacy is a common concern when releasing andsharing data and information. Differential privacy (DP) formalizes privacy inprobabilistic terms without making assumptions about the background knowledgeof data intruders, and thus provides a robust concept for privacy protection.Practical applications of DP involve development of differentially privatemechanisms to generate sanitized results at a pre-specified privacy budget. Forthe sanitization of statistics with publicly known bounds such as proportionsand correlation coefficients, the bounding constraints will need to beincorporated in the differentially private mechanisms. There has been littlework on examining the consequences of the bounding constraints on the accuracyof sanitized results and the statistical inferences of the populationparameters based on the sanitized results. In this paper, we formalize thedifferentially private truncated and boundary inflated truncated (BIT)procedures for releasing statistics with publicly known bounding constraints.The impacts of the truncated and BIT Laplace procedures on the statisticalaccuracy and validity of sanitized statistics are evaluated both theoreticallyand empirically via simulation studies.

Statistical Properties of Sanitized Results from Differentially Private Laplace Mechanism with Univariate Bounding Constraints