Elsevier

NeuroImage

Volume 128, March 2016, Pages 413-431
NeuroImage

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

https://doi.org/10.1016/j.neuroimage.2015.11.015Get rights and content
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Highlights

  • 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

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.

Keywords

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

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