Comparing Families of Dynamic Causal Models

• Published in: PLoS computational biology Vol. 6; no. 3; p. e1000709
• Main Authors: Penny, Will D., Stephan, Klaas E., Daunizeau, Jean, Rosa, Maria J., Friston, Karl J., Schofield, Thomas M., Leff, Alex P.
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 01.03.2010; Public Library of Science (PLoS)
• Subjects: Bayes Theorem; Bayesian analysis; Bayesian statistical decision theory; Biology; Brain - physiology; Causality; Combinatorial probabilities; Computational Biology/Computational Neuroscience; Computational Biology/Metabolic Networks; Computational Biology/Systems Biology; Computational Biology/Transcriptional Regulation; Computer Simulation; Geometric probabilities; Inference; Mathematical models; Mathematics/Statistics; Measurement; Medical imaging; Methods; Models, Neurological; Models, Statistical; Nerve Net - physiology; Neuroscience/Cognitive Neuroscience; Neuroscience/Theoretical Neuroscience; Pattern Recognition, Automated - methods; Posterior distributions; Probabilities; Studies; Switzerland; Brain; Computer Simulation; Nerve Net; Bayes Theorem; Models, Neurological; Models, Statistical; Pattern Recognition, Automated; Causality
• ISSN: 1553-7358; 1553-734X; 1553-7358
• DOI: 10.1371/journal.pcbi.1000709

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.