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.

中文翻译：

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接受者操作特征曲线下面积的无模型后验推断

摘要 接收者操作特征曲线 (AUC) 下的面积作为二元分类器性能的总结。对于 AUC 的推断，一个常见的建模假设是双正态性，它限制了分类器产生的分数的分布。然而，这个假设引入了一个无限维的麻烦参数，并且在某些机器学习设置中可能会受到限制。为了避免做出分布假设，并避免完全非参数分析的计算挑战，我们开发了一种直接且无模型的 Gibbs 后验分布，用于对 AUC 进行推理。我们提出了渐近吉布斯后验集中率，以及一种调整学习率的策略，以便相应的可信区间达到名义频率覆盖概率。