Stochastic maximum likelihood mean and cross-spectrum structure estimation: analytic and neuromagnetic Monte Carlo results

In [1] we proposed to analyze cross-spectrum matrices obtained from electroor magneto-encephalographic (EEG/MEG) signals, to obtain estimates of the EEG/MEG sources and their coherence. In this paper we extend this method in two ways. First, by modelling such interactions as linear filters, and second, by taking the mean of the signals across different trials into account. To obtain estimates we propose a stochastic maximum likelihood (SML) method, and obtain the concentrated likelihood that includes the trial means. Keywords—equivalent current dipole, EEG, MEG, stochastic maximum likelihood, array signal processing, mean structure, covariance structures, functional connectivity, effective connectivity