Classical cluster inference is hampered by the spatial specificity paradox. Given the null-hypothesis of no active voxels, the alternative hypothesis states that there is at least one active voxel in a cluster. Hence, the larger the cluster the less we know about where activation in the cluster is. Rosenblatt et al. (2018) proposed a post-hoc inference method, All-resolutions Inference (ARI), that addresses this paradox by estimating the number of active voxels of any brain region. ARI allows users to choose arbitrary brain regions and returns a simultaneous lower confidence bound of the true discovery proportion (TDP) for each of them, retaining control of the family-wise error rate. ARI does not, however, guide users to regions with high enough TDP. In this paper, we propose an efficient algorithm that outputs all maximal supra-threshold clusters, for which ARI gives a TDP lower confidence bound that is at least a chosen threshold, for any number of thresholds that need not be chosen a priori nor all at once. After a preprocessing step in linearithmic time, the algorithm only takes linear time in the size of its output. We demonstrate the algorithm with an application to two fMRI datasets. For both datasets, we found several clusters whose TDP confidently meets or exceeds a given threshold in less than a second.

翻译：经典聚类推断受空间特异性悖论所限。在无活跃体素的原假设下，备择假设认为聚类内至少存在一个活跃体素。因此，聚类范围越大，我们对激活位置的确切认知就越模糊。Rosenblatt等人(2018)提出了一种事后推断方法——全分辨率推断(ARI)，通过估计任意脑区的活跃体素数量解决了这一悖论。ARI允许用户选择任意脑区，并同时为每个脑区返回真实发现比例(TDP)的同步下界置信区间，同时保持对族系误差率的控制。然而，ARI并未引导用户关注TDP足够高的脑区。本文提出一种高效算法，可输出所有满足ARI给出的TDP下界置信区间不低于选定阈值的最大超阈值聚类，且该算法支持任意数量的阈值，这些阈值无需预先设定或一次性指定。在完成线性对数时间复杂度的预处理后，该算法的运行时间仅与输出规模呈线性关系。我们将该算法应用于两个fMRI数据集进行验证。对这两个数据集，我们均在不到一秒内发现了多个TDP置信度达到或超过给定阈值的聚类。