# Bayesian Model Selection for Group Studies

SPM8 will include a new method for performing a random effects analysis of models at the between-subject or group level. This 2nd-level facility will be added to all DCM modalities (DCM for fMRI, DCM for ERPs etc.). Bayesian model selection (BMS) is a term given to a procedure which identifies the best model among a set of competing models (i.e. the most likely in a set of competing hypotheses). This can be done at the single subject level by examining each model’s log evidence, where the greatest evidence gives the ‘winning’ model. At the second level however, making inferences across the population requires a random-effects treatment that is not sensitive to outliers and accounts for heterogeneity across the population of subjects studied. To this end, a group BMS procedure has been implemented using a Bayesian approach which provides a probability density on the models themselves. This function uses a novel, hierarchical model which specifies a Dirichlet distribution that, in turn, defines the parameters of a multinomial distribution. By sampling from this distribution for each subject we obtain a posterior Dirichlet distribution that specifies the conditional density of the model probabilities. SPM returns the expected multinomial parameters for the models under test which allows users to rank the models from most to least likely at the population level.

K.E. Stephan, W. Penny, J. Daunizeau, R. Moran and K. Friston. Bayesian Model Selection for Group Studies. Under Review.

These descriptions of the new features are taken from the SPM8 Release Notes

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