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An introduction to thermodynamic integration and application to dynamic causal models


Aponte, Eduardo A; Yao, Yu; Raman, Sudhir; Frässle, Stefan; Heinzle, Jakob; Penny, Will D; Stephan, Klaas E (2022). An introduction to thermodynamic integration and application to dynamic causal models. Cognitive Neurodynamics, 16(1):1-15.

Abstract

In generative modeling of neuroimaging data, such as dynamic causal modeling (DCM), one typically considers several alternative models, either to determine the most plausible explanation for observed data (Bayesian model selection) or to account for model uncertainty (Bayesian model averaging). Both procedures rest on estimates of the model evidence, a principled trade-off between model accuracy and complexity. In the context of DCM, the log evidence is usually approximated using variational Bayes. Although this approach is highly efficient, it makes distributional assumptions and is vulnerable to local extrema. This paper introduces the use of thermodynamic integration (TI) for Bayesian model selection and averaging in the context of DCM. TI is based on Markov chain Monte Carlo sampling which is asymptotically exact but orders of magnitude slower than variational Bayes. In this paper, we explain the theoretical foundations of TI, covering key concepts such as the free energy and its origins in statistical physics. Our aim is to convey an in-depth understanding of the method starting from its historical origin in statistical physics. In addition, we demonstrate the practical application of TI via a series of examples which serve to guide the user in applying this method. Furthermore, these examples demonstrate that, given an efficient implementation and hardware capable of parallel processing, the challenge of high computational demand can be overcome successfully. The TI implementation presented in this paper is freely available as part of the open source software TAPAS.

Abstract

In generative modeling of neuroimaging data, such as dynamic causal modeling (DCM), one typically considers several alternative models, either to determine the most plausible explanation for observed data (Bayesian model selection) or to account for model uncertainty (Bayesian model averaging). Both procedures rest on estimates of the model evidence, a principled trade-off between model accuracy and complexity. In the context of DCM, the log evidence is usually approximated using variational Bayes. Although this approach is highly efficient, it makes distributional assumptions and is vulnerable to local extrema. This paper introduces the use of thermodynamic integration (TI) for Bayesian model selection and averaging in the context of DCM. TI is based on Markov chain Monte Carlo sampling which is asymptotically exact but orders of magnitude slower than variational Bayes. In this paper, we explain the theoretical foundations of TI, covering key concepts such as the free energy and its origins in statistical physics. Our aim is to convey an in-depth understanding of the method starting from its historical origin in statistical physics. In addition, we demonstrate the practical application of TI via a series of examples which serve to guide the user in applying this method. Furthermore, these examples demonstrate that, given an efficient implementation and hardware capable of parallel processing, the challenge of high computational demand can be overcome successfully. The TI implementation presented in this paper is freely available as part of the open source software TAPAS.

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Additional indexing

Item Type:Journal Article, refereed, further contribution
Communities & Collections:04 Faculty of Medicine > Institute of Biomedical Engineering
Dewey Decimal Classification:170 Ethics
610 Medicine & health
Scopus Subject Areas:Life Sciences > Cognitive Neuroscience
Uncontrolled Keywords:Cognitive Neuroscience
Language:English
Date:1 February 2022
Deposited On:02 Nov 2021 09:50
Last Modified:25 Apr 2024 01:39
Publisher:Springer
ISSN:1871-4080
OA Status:Hybrid
Free access at:PubMed ID. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/s11571-021-09696-9
PubMed ID:35116083
Project Information:
  • : FunderRené and Susanne Braginsky Foundation
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  • : FunderClinical Research Priority Program “Multiple Sclerosis”
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  • : FunderSNSF
  • : Grant ID320030_179377
  • : Project TitleComputational neuroimaging of predictive coding in interoception
  • : FunderETH Zurich Postdoctoral Fellowship Program
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  • : FunderMarie Curie Actions for People COFUND Program
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  • : FunderETH Zurich
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  • Content: Published Version
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)