Bayesian model reduction and empirical Bayes for group (DCM) studies

• Published in: NeuroImage (Orlando, Fla.) Vol. 128; pp. 413 - 431
• Main Authors: Friston, Karl J., Litvak, Vladimir, Oswal, Ashwini, Razi, Adeel, Stephan, Klaas E., van Wijk, Bernadette C.M., Ziegler, Gabriel, Zeidman, Peter
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01-03-2016; Elsevier Limited; Academic Press
• Subjects: Bayes Theorem; Bayesian analysis; Bayesian model reduction; Biomedical research; Classification; Dynamic causal modelling; Empirical Bayes; Fixed effects; Hierarchical modelling; Humans; Models, Neurological; Normal distribution; Random effects; Schizophrenia; Studies; Technical Note; Empirical Bayes; Hierarchical modelling; Bayesian model reduction; Classification; Random effects; Fixed effects; Dynamic causal modelling
• ISSN: 1053-8119; 1095-9572
• DOI: 10.1016/j.neuroimage.2015.11.015

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.
•We describe a novel scheme for inverting non-linear models (e.g. DCMs) within subjects and linear models at the group level•We demonstrate this scheme is more robust to violations of the (commonly used) Laplace assumption than the standard approach•We validate the approach using a simulated mismatch negativity study of schizophrenia•We demonstrate the application of this scheme to classification and prediction of group membership