Bayesian Brain Edge-Based Connectivity (BBeC): a Bayesian model for brain edge-based connectivity inference

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.