title: Bayesian model reduction and empirical Bayes for group (DCM) studies.
abstract: This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction.
authors.affiliation: The Wellcome Trust Centre for Neuroimaging, UCL, 12 Queen Square, London, UK.
authors.forename: Karl J
authors.initials: KJ
authors.lastname: Friston
authors.affiliation: The Wellcome Trust Centre for Neuroimaging, UCL, 12 Queen Square, London, UK.
authors.forename: Vladimir
authors.initials: V
authors.lastname: Litvak
authors.affiliation: The Wellcome Trust Centre for Neuroimaging, UCL, 12 Queen Square, London, UK.
authors.forename: Ashwini
authors.initials: A
authors.lastname: Oswal
authors.affiliation: The Wellcome Trust Centre for Neuroimaging, UCL, 12 Queen Square, London, UK; Department of Electronic Engineering, NED University of Engineering & Technology, Karachi, Pakistan.
authors.forename: Adeel
authors.initials: A
authors.lastname: Razi
authors.affiliation: The Wellcome Trust Centre for Neuroimaging, UCL, 12 Queen Square, London, UK; Translational Neuromodeling Unit (TNU), Institute for Biomedical Engineering, University of Zurich and ETH Zurich, Switzerland.
authors.forename: Klaas E
authors.initials: KE
authors.lastname: Stephan
authors.affiliation: The Wellcome Trust Centre for Neuroimaging, UCL, 12 Queen Square, London, UK.
authors.forename: Bernadette C M
authors.initials: BCM
authors.lastname: van Wijk
authors.affiliation: The Wellcome Trust Centre for Neuroimaging, UCL, 12 Queen Square, London, UK.
authors.forename: Gabriel
authors.initials: G
authors.lastname: Ziegler
authors.affiliation: The Wellcome Trust Centre for Neuroimaging, UCL, 12 Queen Square, London, UK. Electronic address: peter.zeidman@ucl.ac.uk.
authors.forename: Peter
authors.initials: P
authors.lastname: Zeidman
mesh_terms: D001499:Bayes Theorem; D006801:Humans; D008959:Models, Neurological; D012559:Schizophrenia
keywords: Bayesian model reduction; Classification; Dynamic causal modelling; Empirical Bayes; Fixed effects; Hierarchical modelling; Random effects