  Hypothesis testing is a statistical inference framework for determining the
true distribution among a set of possible distributions for a given dataset.
Privacy restrictions may require the curator of the data or the respondents
themselves to share data with the test only after applying a randomizing
privacy mechanism. This work considers mutual information (MI) as the privacy
metric for measuring leakage. In addition, motivated by the Chernoff-Stein
lemma, the relative entropy between pairs of distributions of the output
(generated by the privacy mechanism) is chosen as the utility metric. For these
metrics, the goal is to find the optimal privacy-utility trade-off (PUT) and
the corresponding optimal privacy mechanism for both binary and m-ary
hypothesis testing. Focusing on the high privacy regime, Euclidean
information-theoretic approximations of the binary and m-ary PUT problems are
developed. The solutions for the approximation problems clarify that an
MI-based privacy metric preserves the privacy of the source symbols in inverse
proportion to their likelihoods.
