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

^{1}, Litvak V

^{1}, Oswal A

^{1}, Razi A

^{2}, Stephan KE

^{3}, van Wijk BCM

^{1}, Ziegler G

^{1}, Zeidman P

^{4}.

### Author information

- 1
- The Wellcome Trust Centre for Neuroimaging, UCL, 12 Queen Square, London, UK.
- 2
- The Wellcome Trust Centre for Neuroimaging, UCL, 12 Queen Square, London, UK; Department of Electronic Engineering, NED University of Engineering & Technology, Karachi, Pakistan.
- 3
- 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.
- 4
- The Wellcome Trust Centre for Neuroimaging, UCL, 12 Queen Square, London, UK. Electronic address: peter.zeidman@ucl.ac.uk.

### 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.

Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

#### KEYWORDS:

Bayesian model reduction; Classification; Dynamic causal modelling; Empirical Bayes; Fixed effects; Hierarchical modelling; Random effects

- PMID:
- 26569570
- PMCID:
- PMC4767224
- DOI:
- 10.1016/j.neuroimage.2015.11.015

- [Indexed for MEDLINE]