Model-free posterior inference on the area under the receiver operating characteristic curve

Abstract

The area under the receiver operating characteristic curve (AUC) serves as a summary of a binary classifier’s performance. For inference on the AUC, a common modeling assumption is binormality, which restricts the distribution of the score produced by the classifier. However, this assumption introduces an infinite-dimensional nuisance parameter and may be restrictive in certain machine learning settings. To avoid making distributional assumptions, and to avoid the computational challenges of a fully nonparametric analysis, we develop a direct and model-free Gibbs posterior distribution for inference on 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 Bayesian methods.