  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.
