Adaptive Cluster Thresholding with Spatial Activation Guarantees Using All-resolutions Inference

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.