发现贝氏-霍奇伯格方法在相关高斯检验中可能失控，挑战了二十年共识。
The Benjamini--Hochberg Procedure Can Fail to Control the FDR for Correlated Two-Sided Gaussian Tests
- 构建相关因子模型，证明在α=0.01时FDR会超过0.0104
- 理论证明在大量假设下FDR突破名义水平，且蒙特卡洛实验验证
- 由AI辅助推导，证实经典FDR控制方法在特定场景失效
我们证明，贝氏-霍奇伯格程序在相关双侧高斯p值情况下，无法在名义水平α=0.01下控制假发现率（FDR）。通过构造一个因子模型，利用区间算术严格证明：当假设数量足够大时，FDR > 0.0104。这一结果反驳了被广泛接受长达二十年的猜想。蒙特卡洛实验结果与理论一致。该证明由GPT-5.6 Pro生成，并经作者仔细核查。
原文摘要 · Abstract (English)
We show that the Benjamini--Hochberg procedure can fail to control the false discovery rate (FDR) at its nominal level for correlated two-sided Gaussian $p$-values. We construct a factor model for which, at level $α=0.01$, a rigorous interval-arithmetic certificate proves $FDR>0.0104$ for all sufficiently large numbers of hypotheses. This disproves a conjecture widely believed to be true for twenty years. Monte Carlo experiments are consistent with the theoretical result. The proof was obtained by GPT-5.6 Pro and carefully checked by the author.
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