  Binary hypothesis testing under the Neyman-Pearson formalism is a statistical
inference framework for distinguishing data generated by two different source
distributions. Privacy restrictions may require the curator of the data or the
data respondents themselves to share data with the test only after applying a
randomizing privacy mechanism. Using mutual information as the privacy metric
and the relative entropy between the two distributions of the output
(postrandomization) source classes as the utility metric (motivated by the
Chernoff-Stein Lemma), this work focuses on finding an optimal mechanism that
maximizes the chosen utility function while ensuring that the mutual
information based leakage for both source distributions is bounded. Focusing on
the high privacy regime, an Euclidean information-theoretic (E-IT)
approximation to the tradeoff problem is presented. It is shown that the
solution to the E-IT approximation is independent of the alphabet size and
clarifies that a mutual information based privacy metric preserves the privacy
of the source symbols in inverse proportion to their likelihood.
