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Empirical Bayes for DCM: A Group Inversion Scheme

Friston, K; Zeidman, P; Litvak, V; (2015) Empirical Bayes for DCM: A Group Inversion Scheme. Frontiers in Systems Neuroscience , 9 p. 164. 10.3389/fnsys.2015.00164. Green open access

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Abstract

This technical note considers a simple but important methodological issue in estimating effective connectivity; namely, how do we integrate measurements from multiple subjects to infer functional brain architectures that are conserved over subjects. We offer a solution to this problem that rests on a generalization of random effects analyses to Bayesian inference about nonlinear models of electrophysiological time-series data. Specifically, we present an empirical Bayesian scheme for group or hierarchical models, in the setting of dynamic causal modeling (DCM). Recent developments in approximate Bayesian inference for hierarchical models enable the efficient estimation of group effects in DCM studies of multiple trials, sessions, or subjects. This approach estimates second (e.g., between-subject) level parameters based on posterior estimates from the first (e.g., within-subject) level. Here, we use empirical priors from the second level to iteratively optimize posterior densities over parameters at the first level. The motivation for this iterative application is to finesse the local minima problem inherent in the (first level) inversion of nonlinear and ill-posed models. Effectively, the empirical priors shrink the first level parameter estimates toward the global maximum, to provide more robust and efficient estimates of within (and between-subject) effects. This paper describes the inversion scheme using a worked example based upon simulated electrophysiological responses. In a subsequent paper, we will assess its robustness and reproducibility using an empirical example.

Type: Article
Title: Empirical Bayes for DCM: A Group Inversion Scheme
Location: Switzerland
Open access status: An open access version is available from UCL Discovery
DOI: 10.3389/fnsys.2015.00164
Publisher version: http://dx.doi.org/10.3389/fnsys.2015.00164
Language: English
Additional information: © 2015 Friston, Zeidman and Litvak. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
Keywords: Bayesian model reduction, dynamic causal modeling, empirical Bayes, fixed effects, hierarchical modeling, random effects
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > UCL Queen Square Institute of Neurology
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > UCL Queen Square Institute of Neurology > Imaging Neuroscience
URI: https://discovery.ucl.ac.uk/id/eprint/1475963
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