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.
翻译:成像数据中外观集的分析对于神经成像学、气候学和宇宙学等一系列广泛的科学学科至关重要。尽管文献越来越多,但关于比较在同一空间区域取样但反映不同研究条件的过程的出版量很少。鉴于一组无症状的高斯随机字段,每个字段与为不同研究条件而采集的样本相对应,这项工作旨在提供所有领域外观集的交叉点或联合点的信任声明。这些空间区域具有自然意义,因为它们直接对应“所有随机字段都超过预定阈值”或“至少有一个随机字段超过预定阈值”的问题。为了评估目前空间变异的程度,我们开发了一种方法,在不假定不同领域之间依赖性的情况下,以预期的信心(即设置交叉点)或断交点(即设定联盟)为定义的空间区域提供分集和超集,同时不假定不同领域之间的依赖性。该方法通过广泛模拟得到验证,并用任务-组合模型显示一个随机字段至少超过预定阈值的场限值”。为了评估现有空间变异度的程度,我们开发了一种由逻辑连接点(即设置交叉点)或断裂变的大脑来确定共同驱动的区域。