Bayesian Image-on-Scalar Regression (ISR) provides flexible, uncertainty-aware neuroimaging analysis. However, applying ISR to large-scale datasets such as the UK Biobank is challenging due to intensive computational demands and the need to handle subject-specific brain masks rather than a common mask. We propose a novel Bayesian ISR model that scales efficiently while accommodating these inconsistent masks. Our method leverages Gaussian process priors with salience area indicators and introduces a scalable posterior computation algorithm using stochastic gradient Langevin dynamics combined with memory mapping. This approach achieves linear scaling with subsample size and constrains memory usage to the batch size, facilitating direct spatial posterior inferences on brain activation regions. Simulation studies and analysis of UK Biobank task fMRI data (38,639 subjects; over 120,000 voxels per image) demonstrate a 4- to 11-fold speed increase and an 8-18% enhancement in statistical power compared to traditional Gibbs sampling with zero-imputation. Our analysis reveals a subregion of the amygdala where emotion-related brain activation decreases by approximately 58% between ages 50 and 60.

翻译：贝叶斯图像对标量回归为神经影像分析提供了灵活且具有不确定性感知能力的方法。然而，将该方法应用于英国生物银行等大规模数据集时，由于计算需求密集且需处理个体特异性脑掩模而非通用掩模，面临巨大挑战。我们提出了一种新颖的贝叶斯图像对标量回归模型，该模型在适应这些不一致掩模的同时实现了高效扩展。我们的方法利用具有显著区域指示器的高斯过程先验，并引入了一种基于随机梯度朗之万动力学与内存映射技术的可扩展后验计算算法。该方法实现了与子样本规模的线性扩展，并将内存使用限制在批次大小范围内，从而促进对大脑激活区域的直接空间后验推断。仿真研究及对英国生物银行任务态功能磁共振成像数据的分析（38,639名受试者；每幅图像超120,000体素）表明，相较于传统零值插补的吉布斯采样方法，本方法实现了4至11倍的速度提升，统计功效提高了8-18%。我们的分析揭示了杏仁核的一个亚区，其中与情绪相关的大脑激活在50至60岁间下降了约58%。