Spatial Confidence Regions for Combinations of Excursion Sets in Image Analysis

TL;DR

This paper develops a statistical method to create confidence regions for the intersection or union of excursion sets across multiple spatially sampled Gaussian fields, useful in neuroimaging and other sciences.

Contribution

It introduces a novel approach for confidence statements about combined excursion sets without assuming dependence between fields, applicable to various scientific disciplines.

Findings

Method verified through extensive simulations.

Successfully applied to fMRI data to identify common brain activation regions.

Provides confidence regions for spatial variability in multiple fields.

Abstract

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.