title: A three domain covariance framework for EEG/MEG data.
abstract: In this paper we introduce a covariance framework for the analysis of single subject EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. Our covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, like in combined EEG-fMRI experiments in which the correlation between EEG and fMRI signals is investigated. We use a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. We apply our method to real EEG and MEG data sets.
authors.affiliation: Department of Mathematics, Faculty of Exact Sciences, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands. Electronic address: b.p.ros@vu.nl.
authors.forename: Beata P
authors.initials: BP
authors.lastname: Roś
authors.affiliation: Department of Mathematics, Faculty of Exact Sciences, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands. Electronic address: f.bijma@vu.nl.
authors.forename: Fetsje
authors.initials: F
authors.lastname: Bijma
authors.affiliation: Department of Mathematics, Faculty of Exact Sciences, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands. Electronic address: m.c.m.de.gunst@vu.nl.
authors.forename: Mathisca C M
authors.initials: MC
authors.lastname: de Gunst
authors.affiliation: Department of Physics and Medical Technology, VU University Medical Center, De Boelelaan 1118, 1081 HZ Amsterdam, The Netherlands. Electronic address: jc.demunck@vumc.nl.
authors.forename: Jan C
authors.initials: JC
authors.lastname: de Munck
mesh_terms: D000328:Adult; D000465:Algorithms; D001921:Brain / Q000502:physiology*; D001931:Brain Mapping / Q000379:methods*; D058256:Brain Waves; D003198:Computer Simulation; D004569:Electroencephalography / Q000379:methods*; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D008279:Magnetic Resonance Imaging / Q000379:methods*; D015225:Magnetoencephalography / Q000379:methods*; D008297:Male; D015203:Reproducibility of Results; D012815:Signal Processing, Computer-Assisted; D055815:Young Adult
keywords: Covariance structure; EEG; Kronecker product structure; MEG; Maximum likelihood; fMRI