A central question in multimodal neuroimaging analysis is to understand the association between two imaging modalities and to identify brain regions where such an association is statistically significant. In this article, we propose a Bayesian nonparametric spatially varying correlation model to make inference of such regions. We build our model based on the thresholded correlation Gaussian process (TCGP). It ensures piecewise smoothness, sparsity, and jump discontinuity of spatially varying correlations, and is well applicable even when the number of subjects is limited or the signal-to-noise ratio is low. We study the identifiability of our model, establish the large support property, and derive the posterior consistency and selection consistency. We also develop a highly efficient Gibbs sampler and its variant to compute the posterior distribution. We illustrate the method with both simulations and an analysis of functional magnetic resonance imaging data from the Human Connectome Project.

翻译：多模态神经影像分析的核心问题在于理解两种成像模态间的关联，并识别此类关联具有统计学显著性的脑区。本文提出一种贝叶斯非参数空间变化相关模型，以对此类区域进行统计推断。该模型基于阈值相关高斯过程构建，能确保空间变化相关性具有分段平滑性、稀疏性和跳跃间断性，即使在被试数量有限或信噪比较低的情况下仍具有良好适用性。我们研究了该模型的可识别性，证明了其大支撑性质，并推导了后验一致性与选择一致性。同时开发了高效吉布斯采样器及其变体用于计算后验分布。通过仿真实验和对人类连接组计划功能磁共振成像数据的分析，验证了该方法的有效性。