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The analysis of excursion sets in imaging data is essential to a wide rangeof scientific disciplines such as neuroimaging, climatology and cosmology.Despite growing literature, there is little published concerning the comparisonof processes that have been sampled across the same spatial region but whichreflect different study conditions. Given a set of asymptotically Gaussianrandom fields, each corresponding to a sample acquired for a different studycondition, this work aims to provide confidence statements about theintersection, or union, of the excursion sets across all fields. Such spatialregions are of natural interest as they directly correspond to the questions"all random fields exceed a predetermined threshold?", or "Where does at leastone random field exceed a predetermined threshold?". To assess the degree ofspatial variability present, we develop a method that provides, with a desiredconfidence, subsets and supersets of spatial regions defined by logicalconjunctions (i.e. set intersections) or disjunctions (i.e. set unions),without any assumption on the dependence between the different fields. Themethod is verified by extensive simulations and demonstrated using a task-fMRIdataset to identify brain regions with activation common to four variants of aworking memory task.

Spatial Confidence Regions for Combinations of Excursion Sets in Image Analysis