Mediation analysis aims to separate the indirect effect through mediators from the direct effect of the exposure on the outcome. It is challenging to perform mediation analysis with neuroimaging data which involves high dimensionality, complex spatial correlations, sparse activation patterns and relatively low signal-to-noise ratio. To address these issues, we develop a new spatially varying coefficient structural equation model for Bayesian Image Mediation Analysis (BIMA). We define spatially varying mediation effects within the potential outcomes framework, employing a soft-thresholded Gaussian process prior for functional parameters. We establish posterior consistency for spatially varying mediation effects along with selection consistency on important regions that contribute to the mediation effects. We develop an efficient posterior computation algorithm scalable to analysis of large-scale imaging data. Through extensive simulations, we show that BIMA can improve the estimation accuracy and computational efficiency for high-dimensional mediation analysis over existing methods. We apply BIMA to analyze behavioral and fMRI data in the Adolescent Brain Cognitive Development (ABCD) study with a focus on inferring the mediation effects of the parental education level on the children's general cognitive ability that are mediated through the working memory brain activity.

翻译：中介分析旨在分离暴露对结果通过中介变量产生的间接效应与直接效应。对神经影像数据进行中介分析具有挑战性，因其涉及高维度、复杂的空间相关性、稀疏的激活模式以及相对较低的信噪比。为解决这些问题，我们开发了一种新的空间变系数结构方程模型，用于贝叶斯图像中介分析（BIMA）。我们在潜在结果框架内定义了空间变化的中介效应，并对功能参数采用了软阈值高斯过程先验。我们建立了空间变化中介效应的后验一致性，以及对贡献于中介效应的重要区域的选取一致性。我们开发了一种高效的后验计算算法，可扩展至大规模影像数据分析。通过大量模拟实验，我们证明BIMA在高维中介分析中相较于现有方法能够提高估计精度和计算效率。我们将BIMA应用于青少年大脑认知发展（ABCD）研究中的行为与功能磁共振成像数据分析，重点推断父母教育水平通过工作记忆脑活动介导的对儿童一般认知能力的中介效应。