The positive false discovery rate:: A Bayesian interpretation and the q-value
The positive false discovery rate:: A Bayesian interpretation and the q-value
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DOI：
10.1214/aos/1074290335
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发表时间：
2003-12-01
影响因子：
4.5
通讯作者：
Storey, JD
中科院分区：
文献类型：
--
作者：
Storey, JD
多重假设检验涉及在同时检验多个假设时控制假阳性率。一种多重假设检验误差度量是错误发现率（FDR），它大致被定义为所有显著假设中假阳性的预期比例。FDR特别适用于探索性分析，在这种分析中，人们有兴趣在许多检验中找到几个显著的结果。在这项工作中，我们引入了FDR的一个修正版本，称为“阳性错误发现率”（pFDR）。我们讨论了pFDR的优缺点，并研究了它的统计特性。当假设检验统计量遵循混合分布时，我们表明pFDR可以写成贝叶斯后验概率，并且可以与分类理论相关联。在相当一般的条件下，即使在某些依赖形式下，这些特性渐近地仍然成立。此外，还引入并研究了一个称为“q值”的新量，它是一种自然的“贝叶斯后验p值”，或者更确切地说，是p值的pFDR类似物。
Multiple hypothesis testing is concerned with controlling the rate of false positives when testing several hypotheses simultaneously. One multiple hypothesis testing error measure is the false discovery rate (FDR), which is loosely defined to be the expected proportion of false positives among all significant hypotheses. The FDR is especially appropriate for exploratory analyses in which one is interested in finding several significant results among many tests. In this work, we introduce a modified version of the FDR called the "positive false discovery rate" (pFDR). We discuss the advantages and disadvantages of the pFDR and investigate its statistical properties. When assuming the test statistics follow a mixture distribution, we show that the pFDR can be written as a Bayesian posterior probability and can be connected to classification theory. These properties remain asymptotically true under fairly general conditions, even under certain forms of dependence. Also, a new quantity called the "q-value" is introduced and investigated, which is a natural "Bayesian posterior p-value," or rather the pFDR analogue of the p-value.