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Comparing families of dynamic causal models.

Penny WD, Stephan KE, Daunizeau J, Rosa MJ, Friston KJ, Schofield TM, Leff AP - PLoS Comput. Biol. (2010)

Bottom Line: Mathematical models of scientific data can be formally compared using Bayesian model evidence.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.

View Article: PubMed Central - PubMed

Affiliation: Wellcome Trust Centre for Neuroimaging, University College, London, United Kingdom. w.penny@fil.ion.ucl.ac.uk

ABSTRACT
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.

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Average Modulatory Connections from RFX for input family P.The figures show the posterior densities of average network parameters from random effects Bayesian model averaging for the modulatory connections. Only forward connections from P to A and from P to F are modulated by speech intelligibility.
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pcbi-1000709-g008: Average Modulatory Connections from RFX for input family P.The figures show the posterior densities of average network parameters from random effects Bayesian model averaging for the modulatory connections. Only forward connections from P to A and from P to F are modulated by speech intelligibility.

Mentions: 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 of the average modulatory connections (averaging over models and subjects). 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.

Penny WD, Stephan KE, Daunizeau J, Rosa MJ, Friston KJ, Schofield TM, Leff AP - PLoS Comput. Biol. (2010)

Average Modulatory Connections from RFX for input family P.The figures show the posterior densities of average network parameters from random effects Bayesian model averaging for the modulatory connections. Only forward connections from P to A and from P to F are modulated by speech intelligibility.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2837394&req=5

pcbi-1000709-g008: Average Modulatory Connections from RFX for input family P.The figures show the posterior densities of average network parameters from random effects Bayesian model averaging for the modulatory connections. Only forward connections from P to A and from P to F are modulated by speech intelligibility.
Mentions: 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 of the average modulatory connections (averaging over models and subjects). 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.

Bottom Line: Mathematical models of scientific data can be formally compared using Bayesian model evidence.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.

View Article: PubMed Central - PubMed

Affiliation: Wellcome Trust Centre for Neuroimaging, University College, London, United Kingdom. w.penny@fil.ion.ucl.ac.uk

ABSTRACT
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.

Show MeSH