Spatial confidence regions for combinations of excursion sets in image analysis.

Area of Science:

• Statistical analysis of imaging data
• Multivariate random field theory
• Applications in neuroimaging, climatology, and cosmology

Background:

• Excursion set analysis is crucial across diverse scientific fields using imaging data.
• Limited research exists on comparing processes sampled under different study conditions within the same spatial region.
• Understanding spatial variability and commonalities across datasets is essential.

Purpose of the Study:

• To develop a method for providing confidence statements on the intersection (all fields) or union (at least one field) of excursion sets.
• To assess spatial variability across different study conditions without assuming field dependence.
• To identify regions where random fields exceed a predetermined threshold under various conditions.

Main Methods:

• Utilizes asymptotically Gaussian random fields representing samples from different study conditions.
• Develops a statistical framework to derive confidence statements for set intersections and unions of excursion sets.
• Employs extensive simulations for verification and demonstrates the method on task-fMRI data.

Main Results:

• The proposed method successfully provides confidence statements for subsets and supersets of spatial regions.
• It quantifies spatial variability and identifies regions of common or unique activation across different task variants.
• Demonstrated effectiveness in identifying brain regions with consistent activation across multiple working memory task conditions.

Conclusions:

• The method offers a robust approach to compare excursion sets from different study conditions in imaging data.
• It enables reliable identification of common or distinct spatial patterns, enhancing inter-study comparisons.
• This technique has significant implications for fields requiring the analysis of complex spatial data under varying experimental designs.