  Estimation of brain functional connectivity (FC) is essential for
understanding the functional organization in the brain and for identifying
changes occurring due to neurological disorders, development, treatment, and
other phenomena. Independent component analysis (ICA) is a matrix decomposition
method that has been used extensively for estimation of brain functional
networks and their FC. However, estimation of FC via ICA is often sub-optimal
due to the use of ad-hoc methods or need for temporal dimension reduction prior
to traditional ICA methods. Bayesian ICA methods can avoid dimension reduction,
produce more accurate estimates, and facilitate inference via posterior
distributions on the model parameters. In this paper, we propose a novel,
computationally efficient Bayesian ICA method with population-derived priors on
both the temporal covariance, representing FC, and the spatial components of
the model. We propose two algorithms for parameter estimation: a Bayesian
Expectation-Maximization algorithm with a Gibbs sampler at the E-step, and a
more computationally efficient variational Bayes algorithm. Through extensive
simulation studies using realistic fMRI data generation mechanisms, we evaluate
the performance of the proposed methods and compare them with existing
approaches. Finally, we perform a comprehensive evaluation of the proposed
methods using fMRI data from over 400 healthy adults in the Human Connectome
Project. Our analyses demonstrate that the proposed Bayesian ICA methods
produce highly accurate measures of functional connectivity and spatial brain
features. The proposed framework is computationally efficient and applicable to
single-subject analysis, making it potentially clinically viable.
