Comparing dynamic causal models using AIC, BIC and free energy
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In neuroimaging it is now becoming standard practise to fit multiple models to data and compare them using a model selection criterion. This is especially prevalent in the analysis of brain connectivity. This paper describes a simulation study which compares the relative merits of three model selection criteria (i) Akaike's Information Criterion (AIC), (ii) the Bayesian Information Criterion (BIC) and (iii) the variational Free Energy. Differences in performance are examined in the context of General Linear Models (GLMs) and Dynamic Causal Models (DCMs). We find that the Free Energy has the best model selection ability and recommend it be used for comparison of DCMs.
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Log model evidence is usually approximated with Bayesian information criteria or variational free energy.
“Practically, log model evidence is usually approximated with Bayesian information criteria or variational free energy (Penny, 2012).”
From Active Inference, homeostatic regulation and adaptive behavioural control (2015) · cites this paper as Penny, 2012
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- Authors
- Penny, W. D.
- Affiliations
- Wellcome Centre for Human Neuroimaging (GB)
- Corresponding author
- Penny, W.D.
- ORCID
- Penny, W.D.
- Venue
- NeuroImage
- Publisher
- Elsevier BV
- Published
- 2012-01
- Volume
- 59
- Issue
- 1
- Pages
- 319-330
- ISSN
- 1053-8119 (ISSN-L)
- PMC
- PMC3200437
- OpenAlex
- W2150847325
- Cited by
- 298
- References
- 47
- Citations by year
- 2026: 10 · 2025: 21 · 2024: 12 · 2023: 16 · 2022: 20 · 2021: 25 · 2020: 26 · 2019: 19 · 2018: 34 · 2017: 23 · 2016: 29 · 2015: 20 · 2014: 16 · 2013: 18 · 2012: 8
- FWCI
- 6.99
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- NeuroImage (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- UCL Discovery (University College London) (submittedVersion)
- UEA Digital Repository (University of East Anglia) (submittedVersion)
- Funders
- Wellcome Trust
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Keywords
- dynamic causal modeling, model selection criteria, Akaike information criterion, Bayesian information criterion, variational free energy, brain connectivity, general linear model, model comparison, simulation study
- MeSH terms
- Bayes Theorem, Brain Mapping, Image Processing, Computer-Assisted, Magnetic Resonance Imaging, Models, Neurological, Models, Theoretical, Reproducibility of Results, Linear Models
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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