Bayesian Estimation of Continuous Brain Connectivity with Log-Gaussian Cox Processes

2026-10-08

AI Summary

This study addresses the limitation of existing kernel smoothing methods for brain connectivity, which yield only point estimates of continuous structural connections without uncertainty quantification. To overcome this, we propose a Bayesian framework that, for the first time, combines log-Gaussian Cox processes with Matérn priors on spherical product spaces. By leveraging finite element representations and Laplace approximation, the method enables efficient posterior inference over ultra-high-dimensional latent variables, thereby producing continuous structural connectivity estimates accompanied by principled uncertainty quantification. Numerical experiments validate both the estimation accuracy and interval coverage of the proposed approach. Furthermore, evaluations on the ABC dataset demonstrate that its leave-one-out fiber bundle prediction performance significantly outperforms conventional kernel smoothing methods.

Abstract

Continuous structural connectivity describes the connection between any two points of the cortical surface by an intensity function. Based on the endpoints of tractography streamlines, existing methods estimate this function mostly by kernel smoothing, which only gives a point estimate. We propose a Bayesian framework that estimates continuous connectivity with uncertainty quantification. The endpoints of tractography streamlines, mapped to two spheres, are modeled by a log-Gaussian Cox process on the product of the spheres with a Matérn Gaussian process prior. With the finite element representation of the prior, the Laplace approximation of the posterior enables the computation on a fine mesh with over 400,000 latent variables per hemisphere pair. Numerical experiments show the accuracy of the point estimate of this approach and the coverage of its credible intervals. In the Adolescent Brain Cognitive Development Study, the proposed method predicts held-out streamlines better than kernel smoothing.

Problem

• continuous brain connectivity
• uncertainty quantification
• tractography streamlines
• point estimate

Innovation

• Bayesian estimation
• Log-Gaussian Cox process
• continuous brain connectivity
• uncertainty quantification
• Laplace approximation