Brain connectivity studies often refer to brain areas as graph nodes and connections between nodes as edges, and aim to identify neuropsychiatric phenotype-related connectivity patterns. When performing group-level brain connectivity alternation analyses, it is critical to model the dependence structure between multivariate connectivity edges to achieve accurate and efficient estimates of model parameters. However, specifying and estimating dependencies between connectivity edges presents formidable challenges because (i) the dimensionality of parameters in the covariance matrix is high (of the order of the fourth power of the number of nodes); (ii) the covariance between a pair of edges involves four nodes with spatial location information; and (iii) the dependence structure between edges can be related to unknown network topological structures. Existing methods for large covariance/precision matrix regularization and spatial closeness-based dependence structure specification/estimation models may not fully address the complexity and challenges. We develop a new Bayesian nonparametric model that unifies information from brain network areas (nodes), connectivity (edges), and covariance between edges by constructing the function of covariance matrix based on the underlying network topological structure. We perform parameter estimation using an efficient Markov chain Monte Carlo algorithm. We apply our method to resting-state functional magnetic resonance imaging data from 60 subjects of a schizophrenia study and simulated data to demonstrate the performance of our method.

中文翻译：

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贝叶斯模型在大脑连接数据中的依赖性。

脑连通性研究通常将大脑区域称为图形节点，并将节点之间的连接称为边缘，旨在识别与神经精神表型相关的连通性模式。在执行组级别的大脑连接性交替分析时，至关重要的是对多元连接性边缘之间的依存关系模型进行建模，以实现对模型参数的准确而有效的估计。但是，由于连通性矩阵中参数的维数很高（约为节点数的四次方），因此指定和估计连通性边缘之间的依赖关系提出了艰巨的挑战。（ii）一对边之间的协方差涉及具有空间位置信息的四个节点；（iii）边缘之间的依存结构可能与未知的网络拓扑结构有关。用于大协方差/精确矩阵正则化和基于空间接近度的依存结构规范/估计模型的现有方法可能无法完全解决复杂性和挑战。我们开发了一种新的贝叶斯非参数模型，该模型通过构造基于基础网络拓扑结构的协方差矩阵的功能来统一来自脑部网络区域（节点），连通性（边缘）和边缘之间的协方差的信息。我们使用高效的马尔可夫链蒙特卡洛算法执行参数估计。我们将我们的方法应用于精神分裂症研究的60名受试者的静止状态功能磁共振成像数据和模拟数据，以证明我们方法的性能。