All-Resolutions Inference for brain imaging

The most prevalent approach to activation localization in neuroimaging is to identify brain regions as contiguous supra-threshold clusters, check their significance using random field theory, and correct for the multiple clusters being tested. Besides recent criticism on the validity of the random field assumption, a spatial specificity paradox remains: the larger the detected cluster, the less we know about the location of activation within that cluster. This is because cluster inference implies "there exists at least one voxel with an evoked response in the cluster", and not that "all the voxels in the cluster have an evoked response". Inference on voxels within selected clusters is considered bad practice, due to the voxel-wise false positive rate inflation associated with this circular inference. Here, we propose a remedy to the spatial specificity paradox. By applying recent results from the multiple testing statistical literature, we are able to quantify the proportion of truly active voxels within selected clusters, an approach we call All-Resolutions Inference (ARI). If this proportion is high, the paradox vanishes. If it is low, we can further "drill down" from the cluster level to sub-regions, and even to individual voxels, in order to pinpoint the origin of the activation. In fact, ARI allows inference on the proportion of activation in all voxel sets, no matter how large or small, however these have been selected, all from the same data. We use two fMRI datasets to demonstrate the non-triviality of the spatial specificity paradox, and its resolution using ARI. We verify that the endless circularity permitted by ARI does not render its estimates overly conservative using both simulation, and a data split.