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