Estimation of cortical multivariate autoregressive models for EEG/MEG using an expectation-maximization algorithm

A new method for estimating multivariate autoregressive (MVAR) models of cortical connectivity from surface EEG or MEG measurements is presented. Conventional approaches to this problem first attempt to solve the inverse problem to estimate cortical signals and then fit an MVAR model to the estimated signals. Our new approach expresses the measured data in tens of a hidden state equation describing MVAR cortical signal evolution and an observation equation that relates the hidden state to the surface measurements. We develop an expectation-maximization (EM) algorithm to find maximum likelihood estimates of the MVAR model parameters. Simulations show that this one-step approach performs significantly better than the conventional two-step approach at estimating the cortical signals and detecting functional connectivity between different cortical regions.