Development of a variational Bayesian expectation maximization (VBEM) method for model inversion of multi-area E/MEG model

We develop and evaluate a variational Bayesian expectation maximization (VBEM) method for model inversion of our multi-area extended neural mass model (MEN) using EEG/MEG data. Parameters of MEN have suitable prior distributions that enable us to use properties of a conjugate-exponential model in implementing VBEM. Consequently, VBEM leads to analytically tractable forms that starts with initialization and consists of repeated iterations of a variational Bayesian expectation step (VB E-step) and a variational Bayesian maximization step (VB M-step). Posterior distributions of model parameters are updated in the VB M-step. Distribution of the hidden state is updated in the VB E-step using variational extended Kalman smoother. We evaluate and validate performance of VBEM method for model inversion of MEN using simulation studies in various signal-to-noise ratios. The proposed approach provides a useful technique for analyzing effective connectivity using non-invasive EEG and MEG methods.