Bayesian estimation for large scale multivariate Ornstein-Uhlenbeck model of brain connectivity
This work addresses the problem of reliable brain connectivity estimation for neuropsychiatric disorder research, but it is incremental as it compares existing methods rather than introducing a new one.
The study tackled the challenge of estimating whole-brain connectivity from limited time samples and high-dimensional data by comparing three methods for the multivariate Ornstein-Uhlenbeck model, finding that the Lyapunov method requires about eight times fewer time samples than the Bayesian method to achieve similar accuracy for networks of around 100 nodes.
Estimation of reliable whole-brain connectivity is a crucial step towards the use of connectivity information in quantitative approaches to the study of neuropsychiatric disorders. When estimating brain connectivity a challenge is imposed by the paucity of time samples and the large dimensionality of the measurements. Bayesian estimation methods for network models offer a number of advantages in this context but are not commonly employed. Here we compare three different estimation methods for the multivariate Ornstein-Uhlenbeck model, that has recently gained some popularity for characterizing whole-brain connectivity. We first show that a Bayesian estimation of model parameters assuming uniform priors is equivalent to an application of the method of moments. Then, using synthetic data, we show that the Bayesian estimate scales poorly with number of nodes in the network as compared to an iterative Lyapunov optimization. In particular when the network size is in the order of that used for whole-brain studies (about 100 nodes) the Bayesian method needs about eight times more time samples than Lyapunov method in order to achieve similar estimation accuracy. We also show that the higher estimation accuracy of Lyapunov method is reflected in a much better classification of individuals based on the estimated connectivity from a real dataset of BOLD fMRI. Finally we show that the poor accuracy of Bayesian method is due to numerical errors, when the imaginary part of the connectivity estimate gets large compared to its real part.