经验贝叶斯预枢轴化在群不变性下的应用：错误发现率控制与调节t检验

中文摘要 AI 辅助

我们考虑同时检验关于数千个单元（如基因或蛋白质）的假设，其中每个单元产生少量重复测量，我们检验其均值是否为零。基因组学中广泛使用的一种方法（在limma软件中实现）跨单元借用强度来学习单元特定方差的分布，然后计算调节t统计量。在这里，我们开发了首批使用调节t统计量的程序，这些程序（i）在单元间独立和零群不变性下，在有限样本中控制错误发现率（FDR），而不假设limma的层次模型，以及（ii）在limma的工作模型下的稀疏渐近机制中，匹配神谕局部错误发现率程序的功效。Benjamini-Hochberg（BH）使用标准t检验p值在同一机制中渐近功效为零。我们的方法从统计量中学习方差分布，这些统计量仅通过单元数据在保持零分布的紧致变换群（如符号翻转或正交旋转）下的轨道来依赖每个单元的数据。然后，我们根据跨单元合并的群变换统计量校准所得的调节t统计量，以获得复合p值，并将其与BH及其紧密变体一起使用。对于小的有限群，我们还使用相同的学习分数构建选择性SeqStep+程序。我们的方法扩展到双样本检验和线性模型系数的检验。

英文摘要

We consider simultaneously testing hypotheses about thousands of units, e.g., genes or proteins, where each unit yields a handful of replicate measurements and we test whether its mean is zero. A widely used approach in genomics, implemented in the limma software, borrows strength across units to learn the distribution of the unit-specific variances, then computes moderated t-statistics. Here we develop the first procedures using moderated t-statistics that (i) control the false discovery rate (FDR) in finite samples under independence across units and null group invariance, without assuming limma's hierarchical model, and (ii) match the power of an oracle local false discovery rate procedure in a sparse asymptotic regime under limma's working model. Benjamini-Hochberg (BH) with standard t-test p-values has asymptotically zero power in the same regime. Our approach learns the variance distribution from statistics that depend on each unit's data only through its orbit under a compact group of transformations that preserves the null distributions, such as sign flips or orthogonal rotations. We then calibrate the resulting moderated t-statistics against group-transformed statistics pooled across units to obtain compound p-values, which we use with BH and a close variant. For small finite groups, we also construct a Selective SeqStep+ procedure using the same learned scores. Our approach extends to two-sample tests and tests of linear model coefficients.

发表机构

• UPMC（巴黎萨克雷大学）

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