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：经典聚类推断受到空间特异性悖论的制约。在无激活体素的零假设下，备择假设认为聚类中至少存在一个激活体素。因此，聚类越大，我们对其中激活位置的认识就越模糊。Rosenblatt等人（2018）提出了一种事后推断方法——全分辨率推断（All-resolutions Inference, ARI），通过估计任意脑区中激活体素的数量来应对这一悖论。ARI允许用户选择任意脑区，并返回每个脑区的真实发现比例（true discovery proportion, TDP）的同步下置信界，同时控制族系错误率。然而，ARI并未引导用户选择具有足够高TDP的脑区。本文提出了一种高效算法，能够输出所有满足ARI给出的TDP下置信界至少达到指定阈值的最大超阈值聚类，且该阈值无需预先设定或一次性指定。经过对数线性时间内的预处理步骤后，该算法仅需线性时间即可输出结果。我们通过两个fMRI数据集的应用验证了该算法。对于这两个数据集，我们在不到一秒内找到了多个TDP稳健达到或超过给定阈值的聚类。