Simultaneous Confidence Regions for Image Excursion Sets: a Validation Study with Applications in fMRI

Functional Magnetic Resonance Imaging (fMRI) is commonly used to localize brain regions activated during a task. Methods have been developed for constructing confidence regions of image excursion sets, allowing inference on brain regions exceeding non-zero activation thresholds. However, these methods have been limited to a single predefined threshold and brain volume data, overlooking more sensitive cortical surface analyses. We present an approach that constructs simultaneous confidence regions (SCRs) which are valid for all possible activation thresholds and are applicable to both volume and surface data. This approach is based on a recent method that constructs SCRs from simultaneous confidence bands (SCBs), obtained by using the bootstrap on 1D and 2D images. To extend this method to fMRI studies, we evaluate the validity of the bootstrap with fMRI data through extensive 2D simulations. Six bootstrap variants, including the nonparametric bootstrap and multiplier bootstrap are compared. The Rademacher multiplier bootstrap-t performs the best, achieving a coverage rate close to the nominal level with sample sizes as low as 20. We further validate our approach using realistic noise simulations obtained by resampling resting-state 3D fMRI data, a technique that has become the gold standard in the field. Moreover, our implementation handles data of any dimension and is equipped with interactive visualization tools designed for fMRI analysis. We apply our approach to task fMRI volume data and surface data from the Human Connectome Project, showcasing the method's utility.