Statistical analysis of multimodal imaging data is a challenging task, since the data involves high-dimensionality, strong spatial correlations and complex data structures. In this paper, we propose rigorous statistical testing procedures for making inferences on the complex dependence of multimodal imaging data. Motivated by the analysis of multi-task fMRI data in the Human Connectome Project (HCP) study, we particularly address three hypothesis testing problems: (a) testing independence among imaging modalities over brain regions, (b) testing independence between brain regions within imaging modalities, and (c) testing independence between brain regions across different modalities. Considering a general form for all the three tests, we develop a global testing procedure and a multiple testing procedure controlling the false discovery rate. We study theoretical properties of the proposed tests and develop a computationally efficient distributed algorithm. The proposed methods and theory are general and relevant for many statistical problems of testing independence structure among the components of high-dimensional random vectors with arbitrary dependence structures. We also illustrate our proposed methods via extensive simulations and analysis of five task fMRI contrast maps in the HCP study.

翻译：多模态成像数据的统计分析是一项具有挑战性的任务，因为这类数据具有高维性、强空间相关性和复杂的数据结构。本文针对多模态成像数据的复杂依赖关系推断，提出了严格的统计检验方法。受人类连接组计划（HCP）研究中多任务fMRI数据分析的启发，我们特别处理了三个假设检验问题：（a）检验脑区间成像模态间的独立性；（b）检验同一成像模态下脑区间的独立性；（c）检验不同模态下脑区间的独立性。针对三个检验的通用形式，我们开发了全局检验程序及控制错误发现率的多重检验程序。我们研究了所提出检验的理论性质，并开发了计算高效的分布式算法。本文提出的方法与理论具有普适性，适用于高维随机向量分量间具有任意依赖结构的独立性检验问题。我们通过大量模拟实验及对HCP研究中五个任务fMRI对比图的分析，进一步验证了所提方法的效果。