Bayesian model selection for group studies

Bayesian model selection for group studies

2009 | Stephan, K E ; Penny, W D ; Daunizeau, J ; Moran, R J ; Friston, K J
The paper introduces a novel approach for Bayesian model selection (BMS) at the group level, which is particularly useful in neuroimaging studies, especially those involving dynamic causal modeling (DCM). The authors compare the group Bayes factor (GBF), a commonly used metric, with two random effects methods for BMS at the between-subject level. The first method uses classical (frequentist) inference on log-evidences, while the second method employs a hierarchical Bayesian model optimized to provide a probability density on the models themselves. The hierarchical Bayesian approach treats the model as a random variable and estimates the parameters of a Dirichlet distribution, which describes the probabilities for all models. This allows for the computation of how likely it is that a specific model generated the data of a randomly selected subject, and it is more robust to outliers compared to the GBF and frequentist tests. The paper demonstrates the advantages of the new Bayesian approach using both synthetic and empirical data. In synthetic data, the method correctly identified the correct model in 100% of cases, while the GBF was influenced by an outlier subject. In empirical data, the Bayesian method accurately identified the superior model in two cases where frequentist tests failed to detect significant differences. The method also allows for the comparison of specific model attributes or subspaces, providing a more comprehensive assessment of model importance. Overall, the hierarchical Bayesian approach offers a more powerful and robust method for group-level model selection, particularly in the context of DCM and other modeling endeavors in neuroimaging.The paper introduces a novel approach for Bayesian model selection (BMS) at the group level, which is particularly useful in neuroimaging studies, especially those involving dynamic causal modeling (DCM). The authors compare the group Bayes factor (GBF), a commonly used metric, with two random effects methods for BMS at the between-subject level. The first method uses classical (frequentist) inference on log-evidences, while the second method employs a hierarchical Bayesian model optimized to provide a probability density on the models themselves. The hierarchical Bayesian approach treats the model as a random variable and estimates the parameters of a Dirichlet distribution, which describes the probabilities for all models. This allows for the computation of how likely it is that a specific model generated the data of a randomly selected subject, and it is more robust to outliers compared to the GBF and frequentist tests. The paper demonstrates the advantages of the new Bayesian approach using both synthetic and empirical data. In synthetic data, the method correctly identified the correct model in 100% of cases, while the GBF was influenced by an outlier subject. In empirical data, the Bayesian method accurately identified the superior model in two cases where frequentist tests failed to detect significant differences. The method also allows for the comparison of specific model attributes or subspaces, providing a more comprehensive assessment of model importance. Overall, the hierarchical Bayesian approach offers a more powerful and robust method for group-level model selection, particularly in the context of DCM and other modeling endeavors in neuroimaging.
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