  The area under the receiver operating characteristic curve (AUC) serves as a
summary of a binary classifier's performance. Methods for estimating the AUC
have been developed under a binormality assumption which restricts the
distribution of the score produced by the classifier. However, this assumption
introduces an infinite-dimensional nuisance parameter and can be inappropriate,
especially in the context of machine learning. This motivates us to adopt a
model-free Gibbs posterior distribution for the AUC. We present the asymptotic
Gibbs posterior concentration rate, and a strategy for tuning the learning rate
so that the corresponding credible intervals achieve the nominal frequentist
coverage probability. Simulation experiments and a real data analysis
demonstrate the Gibbs posterior's strong performance compared to existing
methods based on a rank likelihood.
