title: Development of a variational scheme for model inversion of multi-area model of brain. Part II: VBEM method.
abstract: In Part I and Part II of these two companion papers (henceforth called Part I and Part II), we develop and evaluate a variational Bayesian expectation maximization (VBEM) method for model inversion of our multi-area extended neural mass model (MEN). In this paper, we develop the VBEM method to estimate posterior distributions of parameters of MEN. We choose suitable prior distributions for the model parameters in order to use properties of a conjugate-exponential model in implementing VBEM. Consequently, VBEM leads to analytically tractable forms. The proposed VBEM algorithm 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 the model parameters are updated in the VB M-step. Distribution of the hidden state is updated in the VB E-step. We develop a variational extended Kalman smoother (VEKS) to infer the distribution of the hidden state in the VB E-step and derive the forward and backward passes of VEKS, analogous to the Kalman smoother. In Part I, we evaluate and validate the VBEM method using simulation studies.
authors.affiliation: Image Analysis Lab., Radiology Department, Henry Ford Hospital, Detroit, MI 48202, USA. abbasb@rad.hfh.edu
authors.forename: Abbas
authors.initials: A
authors.lastname: Babajani-Feremi
authors.forename: Hamid
authors.initials: H
authors.lastname: Soltanian-Zadeh
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D001499:Bayes Theorem; D001921:Brain / Q000166:cytology / Q000502:physiology*; D002540:Cerebral Cortex / Q000166:cytology / Q000502:physiology; D003198:Computer Simulation; D004569:Electroencephalography; D055724:Electrophysiological Phenomena / Q000502:physiology; D006801:Humans; D016013:Likelihood Functions; D015225:Magnetoencephalography; D008959:Models, Neurological; D009415:Nerve Net / Q000166:cytology / Q000502:physiology*; D009474:Neurons / Q000166:cytology / Q000502:physiology; D017711:Nonlinear Dynamics