标题： 经验部分贝叶斯两样本检验 显示英文标题

标题： Empirical partially Bayes two sample testing

摘要： 在高通量生物学中，一个常见的任务是测试成千上万种特征（例如，基因或蛋白质）在两个样本之间的均值差异，通常每个样本只有少量的重复。 稳健t检验通过假设正态性和相等方差来处理这个问题，并应用经验部分贝叶斯原理：为干扰参数（方差）提出并估计先验分布，但不为主要参数（均值）提出先验分布。 这种方法在基因组学中非常成功，但在实践中相等方差假设经常被违反。 同时，在少量重复的情况下，韦尔奇的不等方差t检验会受到类型I错误膨胀和功效低下的影响。 受稳健t检验的启发，我们将经验部分贝叶斯范式扩展到不等方差的两样本检验。 我们开发了两种方法：一种是建模两个样本特定方差的比率，另一种是联合建模两个方差，先验分布通过非参数最大似然估计。 我们的经验部分贝叶斯方法产生的p值在特征数量增加而重复数量保持固定时，渐近上是均匀的，确保渐近类型I错误控制。 模拟和对基因组数据的应用展示了功效的显著提升。 显示英文摘要

摘要： A common task in high-throughput biology is to test for differences in means between two samples across thousands of features (e.g., genes or proteins), often with only a handful of replicates per sample. Moderated t-tests handle this problem by assuming normality and equal variances, and by applying the empirical partially Bayes principle: a prior is posited and estimated for the nuisance parameters (variances) but not for the primary parameters (means). This approach has been highly successful in genomics, yet the equal variance assumption is often violated in practice. Meanwhile, Welch's unequal variance t-test with few replicates suffers from inflated type-I error and low power. Taking inspiration from moderated t-tests, we extend the empirical partially Bayes paradigm to two-sample testing with unequal variances. We develop two procedures: one that models the ratio of the two sample-specific variances and another that models the two variances jointly, with prior distributions estimated by nonparametric maximum likelihood. Our empirical partially Bayes methods yield p-values that are asymptotically uniform as the number of features grows while the number of replicates remains fixed, ensuring asymptotic type-I error control. Simulations and applications to genomic data demonstrate substantial gains in power.