A new approach for fMRI group data analysis is introduced to overcome the limitations of standard voxel-based testing methods, such as Statistical Parametric Mapping (SPM). Using a Bayesian model selection framework, the functional network associated with a certain cognitive task is selected according to the posterior probabilities of mean region activations, given a pre-defined anatomical parcellation of the brain. This approach enables us to control a Bayesian risk that balances false positives and false negatives, unlike the SPM-like approach, which only controls false positives. On data from a mental calculation experiment, it detected the functional network known to be involved in number processing, whereas the SPM-like approach either swelled or missed the different activation regions.