Differential privacy is a de facto standard in data privacy, with
applications in the public and private sectors. A way to explain differential
privacy, which is particularly appealing to statistician and social scientists
is by means of its statistical hypothesis testing interpretation. Informally,
one cannot effectively test whether a specific individual has contributed her
data by observing the output of a private mechanism---any test cannot have both
high significance and high power.
In this paper, we identify some conditions under which a privacy definition
given in terms of a statistical divergence satisfies a similar interpretation.
These conditions are useful to analyze the distinguishability power of
divergences and we use them to study the hypothesis testing interpretation of
some relaxations of differential privacy based on Renyi divergence. This
analysis also results in an improved conversion rule between these definitions
and differential privacy
