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Bayesian model selection for group studies
Open accessAbstract
Bayesian model selection (BMS) is a powerful method for determining the most likely among a set of competing hypotheses about the mechanisms that generated observed data. BMS has recently found widespread application in neuroimaging, particularly in the context of dynamic causal modelling (DCM). However, so far, combining BMS results from several subjects has relied on simple (fixed effects) metrics, e.g. the group Bayes factor (GBF), that do not account for group heterogeneity or outliers. In this paper, we compare the GBF with two random effects methods for BMS at the between-subject or group level. These methods provide inference on model-space using a classical and Bayesian perspective respectively. First, a classical (frequentist) approach uses the log model evidence as a subject-specific summary statistic. This enables one to use analysis of variance to test for differences in log-evidences over models, relative to inter-subject differences. We then consider the same problem in Bayesian terms and describe a novel hierarchical model, which is optimised to furnish a probability density on the models themselves. This new variational Bayes method rests on treating the model as a random variable and estimating the parameters of a Dirichlet distribution which describes the probabilities for all models considered. These probabilities then define a multinomial distribution over model space, allowing one to compute how likely it is that a specific model generated the data of a randomly chosen subject as well as the exceedance probability of one model being more likely than any other model. Using empirical and synthetic data, we show that optimising a conditional density of the model probabilities, given the log-evidences for each model over subjects, is more informative and appropriate than both the GBF and frequentist tests of the log-evidences. In particular, we found that the hierarchical Bayesian approach is considerably more robust than either of the other approaches in the presence of outliers. We expect that this new random effects method will prove useful for a wide range of group studies, not only in the context of DCM, but also for other modelling endeavours, e.g. comparing different source reconstruction methods for EEG/MEG or selecting among competing computational models of learning and decision-making.
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“Such hidden individual differences can be detected by formulating alternative computational models, each reflecting different cognitive strategies, and subjecting them to Bayesian model selection (62).”
From Can Bayesian Theories of Autism Spectrum Disorder Help Improve Clinical Practice? (2016) · cites this paper as [62]
In the citing paper
“As is made clear in [19] the GBF approach implicitly assumes that every subject uses the same model. It is therefore a Fixed Effects analysis.”
From Comparing families of dynamic causal models (2010) · cites this paper as [19]
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“The robustness and accuracy of this method was verified via simulations using data from synthetic populations with known frequencies of competing models [19].”
From Comparing families of dynamic causal models (2010) · cites this paper as [19]
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“Additionally, the use of Gibbs sampling allows us to relax the assumption made in VB that the posterior densities over and factorise [19].”
From Comparing families of dynamic causal models (2010) · cites this paper as [19]
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Metadata
- Authors
- Stephan, K. E., Penny, W. D., Daunizeau, J., Moran, R. J., & Friston, K. J.
- Affiliations
- Wellcome Centre for Human Neuroimaging (GB)
- Corresponding author
- Stephan, Klaas Enno
- Venue
- NeuroImage
- Publisher
- Elsevier BV
- Published
- 2009-07
- Volume
- 46
- Issue
- 4
- Pages
- 1004-1017
- ISSN
- 1053-8119 (ISSN-L)
- PMC
- PMC2703732
- OpenAlex
- W2135173838
- Cited by
- 1,423
- References
- 49
- Citations by year
- 2026: 63 · 2025: 74 · 2024: 76 · 2023: 71 · 2022: 86 · 2021: 100 · 2020: 135 · 2019: 97 · 2018: 102 · 2017: 91 · 2016: 89 · 2015: 109 · 2014: 67 · 2013: 75 · 2012: 59
- FWCI
- 51.46
- Type
- journal article
- Language
- en
- Open access
- green
- www.zora.uzh.ch
- Licence
- Locations
- NeuroImage (publishedVersion)
- PubMed (publishedVersion)
- Zurich Open Repository and Archive (University of Zurich) (acceptedVersion, other-oa)
- PubMed Central (acceptedVersion)
- UCL Discovery (University College London) (submittedVersion)
- Explore Bristol Research (submittedVersion)
- UEA Digital Repository (University of East Anglia) (submittedVersion)
- Zurich Open Repository and Archive (University of Zurich) (submittedVersion, other-oa)
- Zurich Open Repository and Archive (University of Zurich)
- Funders
- Wellcome Trust (056750, 088130)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Keywords
- Bayesian model selection, group study, dynamic causal modeling, random effects, Bayesian hierarchical model, variational inference, outliers, exceedance probability, Dirichlet distribution, model comparison
- MeSH terms
- Algorithms, Bayes Theorem, Brain, Cognition, Diagnostic Imaging, Humans, Models, Neurological
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