富集后验概率的经验Bayes估计
Empirical Bayes estimation of posterior probabilities of enrichment
摘要：
为了解释差异表达的基因或其他发现的特征，研究人员进行假设检验，以确定哪些生物类别，如基因本体论（GO）的生物类别，在发现的特征之间具有差异表示的意义上是丰富的。我们研究应用更好的估计的本地错误发现率（LFDR），概率的生物类别之间的预选功能具有等效的表示。我们确定了三个有前途的估计LFDR检测差分表示：半参数估计（SPE），归一化最大似然估计（NMLE），和最大似然估计（MLE）。我们发现，MLE执行至少以及SPE的顺序为100的GO类别，即使在其基础的混合物模型中的组件的理想数量是未知的。然而，当GO类别的数量与PMM组件的数量相比很小时，MLE是不可靠的。因此，如果类别的数量在10的数量级上，SPE是更可靠的LFDR估计器。NMLE不仅依赖于数据，而且依赖于微分表示的先验概率的特定值。因此，它是一个适当的LFDR估计，只有当GO类别的数量太小的应用程序的其他方法。对于富集检测，我们建议在至少中等数量（~100）的GO类别的情况下通过MLE估计LFDR，在少量GO类别（~10）的情况下通过SPE估计LFDR，在非常少量（~1）的GO类别的情况下通过NMLE估计LFDR。
英文摘要：
To interpret differentially expressed genes or other discovered features, researchers conduct hypothesis tests to determine which biological categories such as those of the Gene Ontology (GO) are enriched in the sense of having differential representation among the discovered features. We study application of better estimators of the local false discovery rate (LFDR), a probability that the biological category has equivalent representation among the preselected features. We identified three promising estimators of the LFDR for detecting differential representation: a semiparametric estimator (SPE), a normalized maximum likelihood estimator (NMLE), and a maximum likelihood estimator (MLE). We found that the MLE performs at least as well as the SPE for on the order of 100 of GO categories even when the ideal number of components in its underlying mixture model is unknown. However, the MLE is unreliable when the number of GO categories is small compared to the number of PMM components. Thus, if the number of categories is on the order of 10, the SPE is a more reliable LFDR estimator. The NMLE depends not only on the data but also on a specified value of the prior probability of differential representation. It is therefore an appropriate LFDR estimator only when the number of GO categories is too small for application of the other methods. For enrichment detection, we recommend estimating the LFDR by the MLE given at least a medium number (~100) of GO categories, by the SPE given a small number of GO categories (~10), and by the NMLE given a very small number (~1) of GO categories.
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