## Section: New Results

### Neuroimaging, Statistical analysis of fMRI data

Participants : Gilles Celeux, Robin Genuer, Merlin Keller, Christine Keribin, Marc Lavielle, Vincent Michel, Jean-Michel Poggi.

This research takes place as part of a collaboration with Neurospin (http://www.math.u-psud.fr/select/reunions/neurospin/Welcome.html ).

Vincent Michel began his PhD in October 2007 under the supervision of Gilles Celeux, Christine Keribin and Bertrand Thirion (Parietal). During his second year of thesis, he studied different ways to introduce spatial information in the features selection techniques, such as developing clustering technique using supervised information. Moreover, he developed an adaptive regularization method, which is estimated within a variational bayes framework ([44] ). Bertrand Thirion and Vincent Michel have also been implied in different neuroscientific studies using classification techniques to improve the analysis of the data : relationship between regions of the brain during mental arithmetic ([15] ), mental representation of quantities ([12] ) and study of the valuation system in the human brain ([16] ).

Moreover, Vincent Michel and Robin Genuer examine the value of random forests to deal with such problems.

Christine Keribin achieved a bibliographical study on the variational methods : describing the principle of variational methods and their applications in the Bayesian inference, surveying the main theoretical results and detailing two examples in the neuroimage field [66] .

Merlin Keller began his PhD in October 2006 under the supervision of Alexis Roche (CEA, Neurospin) and Marc Lavielle. This thesis is dedicated to the statistical analysis of multi-subject fMRI data, with the purpose of identifying bain structures involved in certain cognitive or sensori-motor tasks, in a reproducible way across subjects. To overcome certain limitations of standard voxel-based testing methods, as implemented in the Statistical Parametric Mapping (SPM) software, a Bayesian model selection approach to this problem is used, meaning that the most probable model of cerebral activity given the data is selected from a pre-defined collection of possible models. Based on a parcellation of the brain volume into functionally homogeneous regions, each model corresponds to a partition of the regions into those involved in the task under study and those inactive. This allows to incorporate prior information, and avoids the dependence of the SPM-like approach on an arbitrary threshold, called the clusterforming threshold, to define active regions. By controlling a Bayesian risk, the approach balances false positive and false negative risk control. Furthermore, it is based on a generative model that accounts for the spatial uncertainty on the localization of individual effects, due to spatial normalization errors [42] .