We propose a Bayesian framework for uncertainty quantification and comparison in brain connectivity graph analysis. Standard graph-based approaches typically rely on point estimates of correlation matrices, overlooking the uncertainty induced by high-dimensional estimation from limited data. Our methodology constructs and compares credible hyperrectangles derived from posterior distributions, providing interpretable tools for subject-level inference and longitudinal monitoring. We develop scalable algorithms for estimating these regions in high dimensions and establish theoretical guarantees in the inverse-Wishart model for resting-state fMRI data, including a Bernstein--von Mises theorem for correlation matrices and control of a Bayesian family-wise error rate. The proposed framework enables principled detection of significant connectivity differences both globally and locally while preserving joint dependency structures. While demonstrating competitive performance against multiple-testing procedures on synthetic datasets, our approach also facilitates the direct comparison of two distinct scans from a single patient, a capability currently absent from the literature. We leverage this novelty on real datasets to improve interpretability. Beyond fMRI data, the approach provides a general framework for comparison problems in high-dimensional dependent settings.

翻译：我们提出了一种用于脑连接图分析中不确定性量化与比较的贝叶斯框架。传统基于图的方法通常依赖于相关矩阵的点估计，忽视了从有限数据中进行高维估计所引发的不确定性。我们的方法构建并比较了源自后验分布的置信超矩形，为个体水平推断和纵向监测提供了可解释的工具。我们开发了高维空间中估计这些区域的可扩展算法，并在静息态fMRI数据的逆威沙特模型中建立了理论保证，包括相关矩阵的伯恩斯坦-冯·米泽斯定理以及贝叶斯族系错误率的控制。所提出的框架能够在保持联合依赖结构的同时，在全局和局部层面实现显著连接差异的原理性检测。尽管在合成数据集上与多重检验程序相比展现出竞争性能，我们的方法还实现了对单个患者两次不同扫描的直接比较，这是现有文献中尚不具备的能力。我们利用这一创新在真实数据集上提升了可解释性。除fMRI数据外，该方法为高维相依环境下的比较问题提供了一个通用框架。