  Protection of individual privacy is a common concern when releasing and
sharing data and information. Differential privacy (DP) formalizes privacy in
probabilistic terms without making assumptions about the background knowledge
of data intruders, and thus provides a robust concept for privacy protection.
Practical applications of DP involve development of differentially private
mechanisms to generate sanitized results at a pre-specified privacy budget. For
the sanitization of statistics with publicly known bounds such as proportions
and correlation coefficients, the bounding constraints will need to be
incorporated in the differentially private mechanisms. There has been little
work on examining the consequences of the bounding constraints on the accuracy
of sanitized results and the statistical inferences of the population
parameters based on the sanitized results. In this paper, we formalize the
differentially 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 statistical
accuracy and validity of sanitized statistics are evaluated both theoretically
and empirically via simulation studies.
