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arXiv · 1906.08296

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

Zhe Wang·Ryan Martin
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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.

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Zhe Wang, Ryan Martin. 2019-06-19. Model-free posterior inference on the area under the receiver operating characteristic curve. https://doi.org/10.1016/j.jspi.2020.03.008

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