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

## TL;DR

This paper introduces a model-free Gibbs posterior approach for estimating the AUC of binary classifiers, avoiding restrictive distributional assumptions and providing reliable credible intervals, with strong empirical performance.

## Contribution

It develops a novel model-free Gibbs posterior method for AUC inference, addressing limitations of traditional binormality-based approaches.

## Key findings

- Gibbs posterior achieves accurate AUC estimation without distributional assumptions
- Credible intervals from the Gibbs posterior have nominal frequentist coverage
- Method outperforms existing rank likelihood-based approaches in simulations and real data

## Abstract

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.