一种基于蒙特卡罗的多重检验框架
A Framework for Monte Carlo based Multiple Testing
摘要：
我们关注的是这样一种情况，即我们希望通过检验来检验多个假设，这些检验的p值无法明确计算，但可以使用蒙特卡罗模拟进行近似计算。这种情况在实践中广泛存在。我们感兴趣的是获得与所有假设的p值可用时相同的拒绝和非拒绝。本文通过为一般的多重检验过程提供通用算法，介绍了这种情况的框架。我们建立的条件，保证通过蒙特卡罗模拟获得的拒绝和非拒绝是相同的p值。我们的框架是适用于一般类的步升和步降程序，其中包括许多既定的多重检验校正，如Bonferroni，霍尔姆，Sidak，Hochberg或Benjamini-Hochberg。此外，我们展示了如何使用我们的框架来改进文献中的算法，以便在理论上保证其结果。这些修改可以在实践中容易地实现，并且导致将多重检验结果报告为三个集合连同关于其正确性的误差界限的特定方式，使用真实生物数据集示例性地证明。
英文摘要：
We are concerned with a situation in which we would like to test multiple hypotheses with tests whose p-values cannot be computed explicitly but can be approximated using Monte Carlo simulation. This scenario occurs widely in practice. We are interested in obtaining the same rejections and non-rejections as the ones obtained if the p-values for all hypotheses had been available. The present article introduces a framework for this scenario by providing a generic algorithm for a general multiple testing procedure. We establish conditions which guarantee that the rejections and non-rejections obtained through Monte Carlo simulations are identical to the ones obtained with the p-values. Our framework is applicable to a general class of step-up and step-down procedures which includes many established multiple testing corrections such as the ones of Bonferroni, Holm, Sidak, Hochberg or Benjamini-Hochberg. Moreover, we show how to use our framework to improve algorithms available in the literature in such a way as to yield theoretical guarantees on their results. These modifications can easily be implemented in practice and lead to a particular way of reporting multiple testing results as three sets together with an error bound on their correctness, demonstrated exemplarily using a real biological dataset.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
