Brain connectivity analysis based on magnetic resonance imaging is crucial for understanding neurological mechanisms. However, edge-based connectivity inference faces significant challenges, particularly the curse of dimensionality when estimating high-dimensional covariance matrices. Existing methods often struggle to account for the unknown latent topological structure among brain edges, leading to inaccurate parameter estimation and unstable inference. To address these issues, this study proposes a Bayesian model based on a finite-dimensional Dirichlet distribution. Unlike non-parametric approaches, our method utilizes a finite-dimensional Dirichlet distribution to model the topological structure of brain networks, ensuring constant parameter dimensionality and improving algorithmic stability. We reformulate the covariance matrix structure to guarantee positive definiteness and employ a Metropolis-Hastings algorithm to simultaneously infer network topology and correlation parameters. Simulations validated the recovery of both network topology and correlation parameters. When applied to the Alzheimer's Disease Neuroimaging Initiative dataset, the model successfully identified structural subnetworks. The identified clusters were not only validated by composite anatomical metrics but also consistent with established findings in the literature, collectively demonstrating the model's reliability. The estimated covariance matrix also revealed that intragroup connection strength is stronger than intergroup connection strength. This study introduces a Bayesian framework for inferring brain network topology and high-dimensional covariance structures. The model configuration reduces parameter dimensionality while ensuring the positive definiteness of covariance matrices. As a result, it offers a reliable tool for investigating intrinsic brain connectivity in large-scale neuroimaging studies.

翻译：基于磁共振成像的脑连接性分析对于理解神经机制至关重要。然而，边缘连接性推断面临显著挑战，特别是在估计高维协方差矩阵时的维度灾难问题。现有方法往往难以处理脑边缘之间未知的潜在拓扑结构，导致参数估计不准确且推断不稳定。为解决这些问题，本研究提出了一种基于有限维狄利克雷分布的贝叶斯模型。与非参数方法不同，本方法利用有限维狄利克雷分布对脑网络的拓扑结构进行建模，确保参数维度恒定并提高算法稳定性。我们重构了协方差矩阵结构以保证其正定性，并采用Metropolis-Hastings算法同时推断网络拓扑与相关性参数。仿真实验验证了网络拓扑与相关性参数的可恢复性。在应用于阿尔茨海默病神经影像学倡议数据集时，该模型成功识别了结构子网络。所识别的聚类不仅通过复合解剖指标得到验证，也与文献中已确立的发现相一致，共同证明了模型的可靠性。估计的协方差矩阵还显示组内连接强度高于组间连接强度。本研究提出了一个用于推断脑网络拓扑与高维协方差结构的贝叶斯框架。该模型配置在降低参数维度的同时确保了协方差矩阵的正定性。因此，它为大规模神经影像学研究中的内在脑连接性探索提供了一个可靠工具。