A1647
Title: Quantifying the spatial uncertainty of excursion sets
Authors: Armin Schwartzman - University of California, San Diego (United States) [presenting]
Junting Ren - University of California San Diego (United States)
Fabian Telschow - Humboldt University zu Berlin (Germany)
Abstract: A central problem in image analysis, particularly in brain mapping, is locating the important effects spatially. The standard solution has been to treat it as a large-scale multiple-testing problem. However, this approach assumes signal sparsity and does not provide a measure of spatial uncertainty. It is proposed to directly address the question of where the important effects are by estimating the excursion set where the signal is greater than a threshold. To assess uncertainty, spatial confidence regions are constructed, given as nested sets that spatially bound the true excursion set with a given probability. It is shown that confidence regions with simultaneous control over all excursion thresholds can be obtained by thresholding standard simultaneous confidence bands. This approach is developed for excursion sets of the mean function in a signal-plus-noise model, including coefficients in pointwise regression models, as those used in task fMRI analysis.
