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 outcome framework, employing the soft-thresholded Gaussian process prior for functional parameters. We establish the 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 the existing methods. We apply BIMA to analyze the 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 activities.

翻译：中介分析旨在将暴露因素对结局变量的间接效应（通过中介变量）与直接效应分离开来。由于神经影像数据具有高维度、复杂空间相关性、稀疏激活模式及相对较低的信噪比等特点，对其进行中介分析颇具挑战性。为解决这些问题，我们提出了一种新的空间变系数结构方程模型，用于贝叶斯影像中介分析（BIMA）。我们在潜在结果框架内定义了空间变化的中介效应，并采用软阈值高斯过程先验处理函数参数。我们证明了空间变化中介效应的后验一致性，以及对贡献中介效应的重要区域的选择一致性。我们开发了一种高效的、可扩展至大规模影像数据分析的后验计算算法。通过大量模拟实验，我们证明BIMA能够提高高维中介分析的估计精度和计算效率，优于现有方法。我们将BIMA应用于青少年脑认知发展（ABCD）研究中的行为与功能磁共振成像数据分析，重点关注推断父母教育水平通过工作记忆脑活动对儿童一般认知能力产生的中介效应。