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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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RFX Posterior densities for modulatory families.The histograms show  versus  for the  modulatory families. Modulatory family ‘F’ has the highest posterior expected probability . See Table 2 for other posterior expectations.
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pcbi-1000709-g003: RFX Posterior densities for modulatory families.The histograms show versus for the modulatory families. Modulatory family ‘F’ has the highest posterior expected probability . See Table 2 for other posterior expectations.

Mentions: The first two numerical columns of Table 2 show the posterior family probabilities from an FFX analysis. We can say, with high confidence (total posterior probability, ) that . The last two columns in Table 2 show the posterior expectations and exceedance probabilities from an RFX analysis. These were computed from the posterior densities shown in Figure 3. The conclusions we draw, in this case, are identical to those from the FFX analysis. That is, we can say, with high confidence (total exceedance probability, ) that .


Comparing families of dynamic causal models.

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

RFX Posterior densities for modulatory families.The histograms show  versus  for the  modulatory families. Modulatory family ‘F’ has the highest posterior expected probability . See Table 2 for other posterior expectations.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000709-g003: RFX Posterior densities for modulatory families.The histograms show versus for the modulatory families. Modulatory family ‘F’ has the highest posterior expected probability . See Table 2 for other posterior expectations.
Mentions: The first two numerical columns of Table 2 show the posterior family probabilities from an FFX analysis. We can say, with high confidence (total posterior probability, ) that . The last two columns in Table 2 show the posterior expectations and exceedance probabilities from an RFX analysis. These were computed from the posterior densities shown in Figure 3. The conclusions we draw, in this case, are identical to those from the FFX analysis. That is, we can say, with high confidence (total exceedance probability, ) that .

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