We propose a permutation-based method for testing a large collection of hypotheses simultaneously. Our method provides lower bounds for the number of true discoveries in any selected subset of hypotheses. These bounds are simultaneously valid with high confidence. The methodology is particularly useful in functional Magnetic Resonance Imaging cluster analysis, where it provides a confidence statement on the percentage of truly activated voxels within clusters of voxels, avoiding the well-known spatial specificity paradox. We offer a user-friendly tool to estimate the percentage of true discoveries for each cluster while controlling the family-wise error rate for multiple testing and taking into account that the cluster was chosen in a data-driven way. The method adapts to the spatial correlation structure that characterizes functional Magnetic Resonance Imaging data, gaining power over parametric approaches.

翻译：我们提出一种基于置换的方法，用于同时检验大量假设。该方法可为任意选定的假设子集提供真实发现数量的下界，且这些下界以高置信度同时成立。该方法在功能磁共振成像聚类分析中尤为重要——它能为体素簇内真正激活的体素百分比提供置信陈述，从而规避著名的空间特异性悖论。我们提供一种易用工具，在控制多重检验族系错误率的同时，考虑到集群是通过数据驱动方式选择的，为每个集群估计真实发现百分比。该方法能自适应于功能磁共振成像数据特有的空间相关结构，相较于参数方法具有更强的统计功效。