We explore and compare a variety of definitions for privacy and disclosure
limitation in statistical estimation and data analysis, including (approximate)
differential privacy, testing-based definitions of privacy, and posterior
guarantees on disclosure risk. We give equivalence results between the
definitions, shedding light on the relationships between different formalisms
for privacy. We also take an inferential perspective, where---building off of
these definitions---we provide minimax risk bounds for several estimation
problems, including mean estimation, estimation of the support of a
distribution, and nonparametric density estimation. These bounds highlight the
statistical consequences of different definitions of privacy and provide a
second lens for evaluating the advantages and disadvantages of different
techniques for disclosure limitation.

我们探索和比较了隐私和披露限制的各种定义，在统计估计和数据分析中包括 (近似) 差分隐私、基于测试的隐私定义和对披露风险的后验保证。我们在定义之间给出了等价结果，揭示了不同形式隐私定义之间的关系。我们通过这些定义提供了最小化风险边界的推论视角，包括均值估计，分布支撑的估计和非参数密度估计。这些界限突出了不同隐私定义的统计后果，并为评估不同的披露限制技术的优势和劣势提供了第二个视角。