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Comparing Families of Dynamic Causal Models
Open accessAbstract
Mathematical models of scientific data can be formally compared using Bayesian model evidence. Previous applications in the biological sciences have mainly focussed on model selection in which one first selects the model with the highest evidence and then makes inferences based on the parameters of that model. This "best model" approach is very useful but can become brittle if there are a large number of models to compare, and if different subjects use different models. To overcome this shortcoming we propose the combination of two further approaches: (i) family level inference and (ii) Bayesian model averaging within families. Family level inference removes uncertainty about aspects of model structure other than the characteristic of interest. For example: What are the inputs to the system? Is processing serial or parallel? Is it linear or nonlinear? Is it mediated by a single, crucial connection? We apply Bayesian model averaging within families to provide inferences about parameters that are independent of further assumptions about model structure. We illustrate the methods using Dynamic Causal Models of brain imaging data.
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
The paper proposes family-level Bayesian inference and Bayesian model averaging within families as alternatives to selecting a single best model, especially when many models are compared or subjects may use different models. It illustrates the approach with Dynamic Causal Models of fMRI data from an auditory word-processing study, finding evidence that auditory input enters posterior STS and that speech intelligibility modulates forward connections from P to A and P to F.
Key findings
- Family-level inference avoids brittle best-model selection; family posteriors are invariant to the comparison set under fixed effects, and random-effects family inference is implemented via Gibbs sampling.
- For input connectivity, the FFX posterior for region P alone receiving auditory input was 1.00; RFX expected probability was 0.44 with exceedance probability 0.78, while region A alone had RFX exceedance 0.19.
- For modulatory families, the forward family had the highest FFX posterior (0.64) and RFX expected probability (0.52) with exceedance probability 0.66.
- Bayesian model averaging within input family P showed that only forward connections from P to A and P to F were modulated by speech intelligibility; free-energy-based top models averaged 4.5 modulatory connections versus 2.4 in the earlier AIC/BIC-based study.
Methods
- Dynamic Causal Models for fMRI were used with three regions: left posterior superior temporal sulcus (P), left anterior superior temporal sulcus (A), and pars orbitalis of the inferior frontal gyrus (F); all models had all-to-all endogenous connectivity, with variation in direct input regions and modulatory connections.
- The model space crossed 64 modulatory patterns with 7 input patterns, giving 448 DCMs, fitted to data from a previously published intelligible-speech study; the subject count is not recoverable from the provided text.
- Analysis used fixed-effects and random-effects family-level inference; RFX inference used Gibbs sampling with 10,000 discarded burn-in samples, and Bayesian model averaging was performed within families using Occam’s window.
Limitations
- Stated: the variational Bayes implementation is not accurate for small prior counts, motivating Gibbs sampling; Gibbs sampling is preferred when the number of models exceeds the number of subjects, while VB is preferred for small model sets.
- Stated: the relative merits of different model-evidence criteria are left to a future publication, and the automatic relevance determination approach for DCMs is currently hypothetical.
- Evident from the text: the method is illustrated on one fMRI dataset from an auditory word-processing study, so broader biological applicability is proposed but not tested here; results also depend on the chosen family partitions and on the free-energy approximation to model evidence.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“However, for group random effects inference the ranking of models can be critically dependent on the comparison set.”
§ Comparing Families of Dynamic Causal Models > Materials and Methods > Comparison Set
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“For FFX analysis the relative ranking of a pair of models is not dependent on .”
§ Comparing Families of Dynamic Causal Models > Materials and Methods > Comparison Set
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Second, we emphasise that posterior model probabilities depend on the comparison set.”
§ Comparing Families of Dynamic Causal Models > Materials and Methods > Comparison Set
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In random effects analysis, augmenting the comparison set with a single extra model can, for example, reverse the ranking of the best and second best models.”
§ Comparing Families of Dynamic Causal Models > Introduction
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes? Based: unclearA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Both the RFX and FFX model averages within family P show that only connections from P to A, and from P to F, are facilitated by speech intelligibility.”
§ Comparing Families of Dynamic Causal Models > Results > Model Averaging
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: Under the fixed-effects (FFX) assumption, all subjects use the same model.
- The authors state this as an assumption: Under the random-effects (RFX) assumption, each subject uses their own model.
In the paper
“This is exactly the winning model from earlier work [17] (based on AIC/BIC approximation of model evidence).”
§ Comparing Families of Dynamic Causal Models > Discussion
What the sources say
- Not checked yetcites [17] A Leff, 2008, The cortical dynamics of intelligible speech., J Neurosci source
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Interestingly, the use of BMA produced an average network structure with speech input to region P, and modulatory connections from P to A and from P to F.”
§ Comparing Families of Dynamic Causal Models > Discussion
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“But we can say, with high confidence (total exceedance probability, ) that either region A alone or region P alone receives auditory input.”
§ Comparing Families of Dynamic Causal Models > Results > Input Regions
Load-bearingStrength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: Under the random-effects (RFX) assumption, each subject uses their own model.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This model has input to region P and modulatory connections as shown in Figure 6(a).”
§ Comparing Families of Dynamic Causal Models > Results > Relating Family and Model Levels
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes- The authors state this as an assumption: Under the fixed-effects (FFX) assumption, all subjects use the same model.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The maximum posterior model for the input family inference is model number 185 having posterior probability .”
§ Comparing Families of Dynamic Causal Models > Results > Relating Family and Model Levels
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes- The authors state this as an assumption: Under the fixed-effects (FFX) assumption, all subjects use the same model.
- Probably not a substantial claim. 15
- It may state two separate claims as one. 22
- The quote only partly states this claim. 4
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Figure 7 shows the posterior densities of average modulatory connections (averaging over models and subjects). The height of the delta functions in these histograms correspond to the total posterior probability mass of models which assume that the connection is zero.”
§ Comparing Families of Dynamic Causal Models > Results > Model Averaging
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- The authors state this as an assumption: Under the fixed-effects (FFX) assumption, all subjects use the same model.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The worst one is with . The posterior odds of the best relative to the worst is only (the largest it could be is ), meaning these models are not significantly better than one another.”
§ Comparing Families of Dynamic Causal Models > Results > Model Averaging
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: Under the fixed-effects (FFX) assumption, all subjects use the same model.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Out of these two possibilities it is much more likely that region P alone receives auditory input (exceedance probability ) rather than region A (exceedance probability ).”
§ Comparing Families of Dynamic Causal Models > Results > Input Regions
Load-bearingStrength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one. The quote only partly states this claim.
- The authors state this as an assumption: Under the random-effects (RFX) assumption, each subject uses their own model.
In the paper
“It turns out that although the variational algorithm is robust for , it is not accurate for .”
§ Comparing Families of Dynamic Causal Models > Materials and Methods > Random Effects Analysis
What the sources say
- Not checked yetcites Text S1
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For RFX inference the input was inferred to most likely enter region P alone (posterior exceedance probability, ). In the RFX model averaging the Occam's windowing procedure was specific to each subject, thus each subject can have a different number of models in Occam's window. For the input model P family there were an average of models in Occam's window and Figure 8 shows the posterior densities”
§ Comparing Families of Dynamic Causal Models > Results > Model Averaging
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one. The quote only partly states this claim.
- The authors state this as an assumption: Under the random-effects (RFX) assumption, each subject uses their own model.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“| Forward, | 0.64 | −0.44 | 0.52 | 0.66 |”
§ Comparing Families of Dynamic Causal Models > Results > Forward versus Backward
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one. The quote only partly states this claim.
- The authors state this as an assumption: Under the fixed-effects (FFX) assumption, all subjects use the same model.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For FFX inference the input was inferred to enter region P only. We therefore restrict the averaging to those 64 models in family P. This produces 16 models in Occam's window (itself indicating that the posterior is not sharply peaked).”
§ Comparing Families of Dynamic Causal Models > Results > Model Averaging
Strength:hedged· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: Under the fixed-effects (FFX) assumption, all subjects use the same model.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The model with the highest free energy (see figure 6(a)) does not, however, have significantly higher evidence than the second best model, or indeed, any model in Occam's window.”
§ Comparing Families of Dynamic Causal Models > Discussion
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This ‘best model’ approach is very useful but, as we shall see, can become brittle if there are a large number of models to compare, or if in the analysis of data from a group of subjects, different subjects use different models (as is the case for a random effects analysis [19]).”
§ Comparing Families of Dynamic Causal Models > Introduction
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Family level inference removes uncertainty about aspects of model structure other than the characteristic of interest.”
§ Comparing Families of Dynamic Causal Models > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✗ Based: failsProbably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If one were to group the models based on this characteristic then the inference about the characteristic would be robust.”
§ Comparing Families of Dynamic Causal Models > Materials and Methods > Comparison Set
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✗ Based: failsProbably not a substantial claim. The paper may give no reason why it holds.
In the paper
“The number of models in the window, , is a useful indicator as smaller values correspond to peakier posteriors.”
§ Comparing Families of Dynamic Causal Models > Materials and Methods > Bayesian Model Averaging
What the sources say
- Not checked yetcites [38] D Madigan, 1994, Model selection and accounting for uncertainty in graphical models using Occam's window., Journal of the American Statistical Association source
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Family level inference removes uncertainty about aspects of model structure other than the characteristic one is interested in.”
§ Comparing Families of Dynamic Causal Models > Discussion
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✗ Based: failsProbably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Our results indicate that spoken words most likely stimulate a region in posterior STS and that if the word is intelligible connections are strengthened both to anterior STS and an inferior frontal region.”
§ Comparing Families of Dynamic Causal Models > Discussion
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The family level inference procedures described in this paper can be applied whatever method is used for estimating the model evidence.”
§ Comparing Families of Dynamic Causal Models > Discussion
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
In the 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.”
§ Comparing Families of Dynamic Causal Models > Materials and Methods > Fixed Effects Analysis
What the sources say
- Not checked yetcites [19] K Stephan, 2009, Bayesian model selection for group studies., Neuroimage source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We have shown that this ‘best model’ approach, though useful when the number of models is small, can become brittle if there are a large number of models, and if different subjects use different models.”
§ Comparing Families of Dynamic Causal Models > Discussion
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This is because it is important that the total prior count, , does not dominate over the number of subjects, otherwise posterior densities will be dominated by the prior rather than the data.”
§ Comparing Families of Dynamic Causal Models > Materials and Methods > Random Effects Analysis
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes? Based: unclearIt may state two separate claims as one.
In the paper
“In other comparisons, based on simulation of graphical model structures [6] the Free Energy method approached the performance of AIS and clearly outperformed BIC.”
§ Comparing Families of Dynamic Causal Models > Materials and Methods > Model Evidence
What the sources say
- Not checked yetcites [6] M Beal, 2003, The Variational Bayesian EM algorithms for incomplete data: with application to scoring graphical model structures. source
Strength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“Previous work in graphical models favours the free energy approach over BIC [6] and work on biochemical models finds AIS to be the best of the more computationally expensive sampling methods.”
§ Comparing Families of Dynamic Causal Models > Discussion
What the sources say
- Not checked yetcites [6] M Beal, 2003, The Variational Bayesian EM algorithms for incomplete data: with application to scoring graphical model structures. source
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This means the posteriors can be multimodal and are most simply evaluated by sampling.”
§ Comparing Families of Dynamic Causal Models > Materials and Methods > Bayesian Model Averaging
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“Before proceeding we note that the use of Bayesian model averaging is a standard approach in the field of Bayesian statistics [4], but has yet to be applied extensively in computational biology.”
§ Comparing Families of Dynamic Causal Models > Introduction
What the sources say
- Not checked yetcites [4] J Hoeting, 1999, Bayesian Model Averaging: A Tutorial., Statistical Science
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We emphasise that the use of Occam's window is for computational expedience only.”
§ Comparing Families of Dynamic Causal Models > Materials and Methods > Bayesian Model Averaging
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“The use of model families is also accomodated naturally within the framework of hierarchical Bayesian models [1] and is proposed to address the well known issue of model dilution [4].”
§ Comparing Families of Dynamic Causal Models > Introduction
What the sources say
- Not checked yetcites [1] A Gelman, 1995, Bayesian Data Analysis source
- Not checked yetcites [4] J Hoeting, 1999, Bayesian Model Averaging: A Tutorial., Statistical Science
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Given that all families have the same number of members, the model priors are uniform, so the maximum posterior model is also the one with highest aggregate model evidence.”
§ Comparing Families of Dynamic Causal Models > Results > Relating Family and Model Levels
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“From equations 13 and 22 we see that this can be achieved by setting(24)”
§ Comparing Families of Dynamic Causal Models > Materials and Methods > Family Inference
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe quote only partly states this claim.
In the paper
“This is to be compared with the free energy approach in which the complexity penalty is given by the KL-divergence between the prior and approximate posterior [11]. This allows parameters to be differentially penalised.”
§ Comparing Families of Dynamic Causal Models > Materials and Methods > Model Evidence
What the sources say
- Not checked yetcites [11] W Penny, 2004, Comparing Dynamic Causal Models., NeuroImage source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As we shall see in the following section, unbiased family level inferences require uniform priors over families.”
§ Comparing Families of Dynamic Causal Models > Materials and Methods > Random Effects Analysis
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✗ Based: failsProbably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This indicates that in the particular example we have studied the use of Bayes factors or posterior odds ratios would be inconclusive, whereas clear conclusions can be drawn from family level inference.”
§ Comparing Families of Dynamic Causal Models > Discussion
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Family level inferences under RFX assumptions are more subtle and have been the main focus of this paper.”
§ Comparing Families of Dynamic Causal Models > Discussion
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✗ Checkable: fails✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may be too vague to check against evidence. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Additionally, Bayesian Model Averaging can be used with the Discrete approach to provide estimates of the marginal density .”
§ Comparing Families of Dynamic Causal Models > Discussion
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The issue of family versus model level inference is orthogonal to the issue of random versus fixed effects analysis.”
§ Comparing Families of Dynamic Causal Models > Discussion
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The same critera re. FFX versus RFX apply at the family level as at the model level.”
§ Comparing Families of Dynamic Causal Models > Discussion
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Family level inferences under FFX assumptions are simple to implement.”
§ Comparing Families of Dynamic Causal Models > Discussion
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The authors state this as an assumption.
The Free Energy bound is tight.
“Under the assumption that this bound is tight, model comparison can then proceed using as a surrogate for the log-model evidence.”
The authors state this as an assumption.
Under the fixed-effects (FFX) assumption, all subjects use the same model.
“We could take this to be under the FFX assumption that all subjects use the same model, or under the RFX assumption that each subject uses their own model (see equation 14).”
The authors state this as an assumption.
Under the random-effects (RFX) assumption, each subject uses their own model.
“We could take this to be under the FFX assumption that all subjects use the same model, or under the RFX assumption that each subject uses their own model (see equation 14).”
The paper relies on this without support.
Dynamic causal models (DCMs) have a Gaussian form.
“For the applications in this paper, the posterior densities from equation 27 will therefore correspond to a mixture of delta functions and Gaussians because for DCMs have a Gaussian form.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“However, in recent years, the number of models over which people search (the model-space) has grown enormously; to the extent that DCM is now used to discover the best model over very large model-spaces (e.g., Stephan et al., 2010; Penny et al., 2010).”
From Network discovery with DCM (2011) · cites this paper as Penny et al., 2010
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
PAF model range overlaps other input families
MinorThe stated PAF range (285-448) overlaps PA (257-320) and PF (321-384). That contradicts the requirement that family subsets be non-overlapping.
“These are family A (models 1 to 64), F (65 to 128), P (129 to 192), AF (193 to 256), PA (257 to 320), PF (321 to 384) and PAF (285 to 448).”
“The subsets must be non-overlapping and their union must be equal to S.”
Citations
Cites
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Gudgeon, A. C., & Howell, D. C. (1994) · Journal of the Royal Statistical Society Series D (The Statistician) · doi:10.2307/2348956 · Cited by 8,277
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Information Theory, Inference, and Learning Algorithms
(2004) · Kybernetes · doi:10.1108/03684920410534506 · Cited by 4,937
Friston, K. J., Harrison, L., & Penny, W. (2003) · NeuroImage · doi:10.1016/s1053-8119(03)00202-7 · Cited by 4,583
Self-citationHoeting, J. A., Madigan, D., Raftery, A. E., & Volinsky, C. T. (1999) · Statistical Science · doi:10.1214/ss/1009212519 · Cited by 4,118
Statistical Parametric Mapping: The Analysis of Functional Brain Images
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“BMC at the group level, also known as random effects model [101,102], has become a standard statistical test in the fields of neuroimaging and behavioral modeling ([101] cited> 250 times).”
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Self-citationFunctional Evidence for a Dual Route to Amygdala
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Self-citationCross-language differences in the brain network subserving intelligible speech
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The Known Unknowns: Neural Representation of Second-Order Uncertainty, and Ambiguity
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Self-citationfMRI Functional Connectivity Applied to Adolescent Neurodevelopment
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Dynamic causal modeling with neural fields
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Self-citationReading Front to Back: MEG Evidence for Early Feedback Effects During Word Recognition
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Self-citationWorking memory load modulation of parieto‐frontal connections: Evidence from dynamic causal modeling
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Self-citationAtomoxetine restores the response inhibition network in Parkinson’s disease
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Self-citation
Metadata
- Authors
- Penny, W. D., Stephan, K. E., Daunizeau, J., Rosa, M. J., Friston, K. J., Schofield, T. M., & Leff, A. P.
- Affiliations
- Wellcome Centre for Human Neuroimaging (GB)
- Corresponding author
- Penny, Will D.
- Venue
- PLoS Computational Biology
- Publisher
- Public Library of Science (PLoS)
- Published
- 2010-03-12
- Volume
- 6
- Issue
- 3
- Pages
- e1000709
- ISSN
- 1553-734X (ISSN-L)
- 1553-7358
- PMC
- PMC2837394
- OpenAlex
- W1998151455
- Semantic Scholar
- 2f88070d894eb8d1a96c8f92c726f0422f3bcccd
- Cited by
- 688
- References
- 46
- Citations by year
- 2026: 13 · 2025: 35 · 2024: 25 · 2023: 25 · 2022: 33 · 2021: 51 · 2020: 54 · 2019: 36 · 2018: 43 · 2017: 47 · 2016: 57 · 2015: 71 · 2014: 43 · 2013: 67 · 2012: 36
- FWCI
- 29.48
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- PLoS Computational Biology (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Research Portal (King's College London) (publishedVersion, other-oa)
- Zurich Open Repository and Archive (University of Zurich) (acceptedVersion, cc-by)
- RePEc: Research Papers in Economics (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- UCL Discovery (University College London) (submittedVersion)
- UEA Digital Repository (University of East Anglia) (submittedVersion)
- Zurich Open Repository and Archive (University of Zurich) (submittedVersion, cc-by)
- Zurich Open Repository and Archive (University of Zurich)
- Funders
- Wellcome Trust (088130)
- Universität Zürich
- 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 Bayesian Inference
- Keywords
- dynamic causal modeling, Bayesian model averaging, model comparison, marginal likelihood, neuroimaging, parameter uncertainty, model structure uncertainty
- MeSH terms
- Bayes Theorem, Brain, Computer Simulation, Models, Neurological, Nerve Net, Pattern Recognition, Automated, Models, Statistical, Causality
About these checks
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.
A language model drew the claims from the paper on 2026-10-09, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-09 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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