Cluster inference based on spatial extent thresholding is a popular analysis method multiple testing in spatial data, and is frequently used for finding activated brain areas in neuroimaging.... Show moreCluster inference based on spatial extent thresholding is a popular analysis method multiple testing in spatial data, and is frequently used for finding activated brain areas in neuroimaging. However, the method has several well-known issues. While powerful for finding regions with some activation, the method as currently defined does not allow any further quantification or localisation of signal. In this paper, we repair this gap. We show that cluster-extent inference can be used (1) to infer the presence of signal in any region of interest and (2) to quantify the percentage of activation in such regions. These additional inferences come for free, i.e. they do not require any further adjustment of the alpha-level of tests, while retaining full family-wise error control. We achieve this extension of the possibilities of cluster inference by embedding the method into a closed testing procedure, and solving the graph-theoretic k-separator problem that results from this embedding. We demonstrate the usefulness of the improved method in a large-scale application to neuroimaging data from the Neurovault database. Show less
Sum-based global tests are highly popular in multiple hypothesis testing. In this paper, we propose a general closed testing procedure for sum tests, which provides lower confidence bounds for the... Show moreSum-based global tests are highly popular in multiple hypothesis testing. In this paper, we propose a general closed testing procedure for sum tests, which provides lower confidence bounds for the proportion of true discoveries (TDPs), simultaneously over all subsets of hypotheses. These simultaneous inferences come for free, i.e., without any adjustment of the α-level, whenever a global test is used. Our method allows for an exploratory approach, as simultaneity ensures control of the TDP even when the subset of interest is selected post hoc. It adapts to the unknown joint distribution of the data through permutation testing. Any sum test may be employed, depending on the desired power properties. We present an iterative shortcut for the closed testing procedure, based on the branch and bound algorithm, which converges to the full closed testing results, often after few iterations; even if it is stopped early, it controls the TDP. We compare the properties of different choices for the sum test through simulations, then we illustrate the feasibility of the method for high-dimensional data on brain imaging and genomics data. Show less
