MMCTest --一种安全的多蒙特卡罗检验算法
MMCTest - A Safe Algorithm for Implementing Multiple Monte Carlo Tests
摘要：
考虑使用只能通过模拟评估的测试来测试多个假设，例如排列测试或自助测试。本文介绍了MMCTest，一种顺序算法，它以任意高的概率给出与适用于理想p值的特定多重检验程序相同的分类。该方法可以与一类多重检验程序一起使用，其中包括Benjamini & Hochberg错误发现率（FDR）程序和控制Familywise错误率的Bonferroni校正。该算法的一个关键特征是，它停止对所有已经被决定为被拒绝或未被拒绝的假设进行采样。MMCTest可以在任何阶段中断，然后返回三组假设：拒绝的，未拒绝的和未决定的假设。由实际生物数据激发的模拟研究表明，MMCTest在实践中是可用的，尽管有额外的保证，它可以比其他方法更有效的计算。
英文摘要：
Consider testing multiple hypotheses using tests that can only be evaluated by simulation, such as permutation tests or bootstrap tests. This article introduces MMCTest, a sequential algorithm which gives, with arbitrarily high probability, the same classification as a specific multiple testing procedure applied to ideal p-values. The method can be used with a class of multiple testing procedures which includes the Benjamini & Hochberg False Discovery Rate (FDR) procedure and the Bonferroni correction controlling the Familywise Error Rate. One of the key features of the algorithm is that it stops sampling for all the hypotheses which can already be decided as being rejected or non-rejected. MMCTest can be interrupted at any stage and then returns three sets of hypotheses: the rejected, the non-rejected and the undecided hypotheses. A simulation study motivated by actual biological data shows that MMCTest is usable in practice and that, despite the additional guarantee, it can be computationally more efficient than other methods.
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