Multiple hypothesis testing (MHT) frequently arises in scientific inquiries, and concurrent testing of multiple hypotheses inflates the risk of Type-I errors or false positives, rendering MHT corrections essential. This paper addresses MHT in the context of conformal prediction, a flexible framework for predictive uncertainty quantification. Some conformal applications give rise to simultaneous testing, and positive dependencies among tests typically exist. We introduce $\texttt{max-rank}$, a novel correction that exploits these dependencies whilst efficiently controlling the family-wise error rate. Inspired by existing permutation-based corrections, $\texttt{max-rank}$ leverages rank order information to improve performance and integrates readily with any conformal procedure. We establish its theoretical and empirical advantages over the common Bonferroni correction and its compatibility with conformal prediction, highlighting the potential to strengthen predictive uncertainty estimates.

翻译：多重假设检验在科学研究中频繁出现，同时检验多个假设会增大I类错误（即假阳性）的风险，因此多重检验校正确保统计推断的有效性至关重要。本文针对Conformal Prediction（一种灵活的预测不确定性量化框架）中的多重检验问题展开研究。部分Conformal应用场景会引发同步检验，且检验间通常存在正相关性。我们提出一种新颖的校正方法$\texttt{max-rank}$，该方法在有效控制族错误率的同时充分利用了检验间的相关性。受现有基于置换的校正方法启发，$\texttt{max-rank}$利用秩次信息提升检验效能，并可无缝集成于各类Conformal流程。我们通过理论证明与实证分析，阐明了该方法相较于传统Bonferroni校正的优越性及其与Conformal Prediction框架的兼容性，凸显了其在强化预测不确定性估计方面的潜力。