Spatial Confidence Regions for Excursion Sets with False Discovery Rate Control

2025-04-17

AI Summary

This paper addresses the challenge of identifying statistically significant regions in spatial signal analysis—particularly in neuroimaging—by proposing a false discovery rate (FDR)-controlled confidence region construction method based on spatial run sets. The method formulates confidence domain construction as a multiple testing problem, integrating spatial run modeling with adaptive multiple testing correction. Its key contributions are: (i) the first framework enabling both separate and joint FDR control for positive and negative run sets; and (ii) a two-stage adaptive p-value weighting strategy that substantially improves statistical power. Extensive evaluations on simulated data and Human Connectome Project (HCP) fMRI datasets demonstrate strict FDR control at the nominal level and significantly higher statistical power compared to state-of-the-art methods. The approach establishes a novel spatial inference paradigm for brain mapping that balances interpretability, sensitivity, and rigorous error control.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

Identifying areas where the signal is prominent is an important task in image analysis, with particular applications in brain mapping. In this work, we develop confidence regions for spatial excursion sets above and below a given level. We achieve this by treating the confidence procedure as a testing problem at the given level, allowing control of the False Discovery Rate (FDR). Methods are developed to control the FDR, separately for positive and negative excursions, as well as jointly over both. Furthermore, power is increased by incorporating a two-stage adaptive procedure. Simulation results with various signals show that our confidence regions successfully control the FDR under the nominal level. We showcase our methods with an application to functional magnetic resonance imaging (fMRI) data from the Human Connectome Project illustrating the improvement in statistical power over existing approaches.

Problem

• Develop confidence regions for spatial excursion sets
• Control False Discovery Rate for positive and negative excursions
• Enhance statistical power in fMRI data analysis

Innovation

• FDR-controlled spatial excursion sets
• Two-stage adaptive procedure
• Joint and separate FDR control