Multigrid Priors for fMRI time series analysis

We deal with the problem of constructing, priors for data analysis in order to asses brain activity in functional Magnetic Resonance Imaging (fMRI). Our method is an example of how a prior distribution can incorporate what Could be termed as conventional prior information as well as other information Such as that steming from knowledge of what constitues a reasonable likelihood. Brain activity during a cognitive. sensorial or motor task presents a certain level of localization and spatial correlations with different scales involved in the problem. These Suggests a multiscale iterative procedure to construct the prior. Grids of different scales are constructed over the image. Spatially coarse grain data variables are defined for each scale. until a single voxel time series is obtained. The process consists in iterating back to finer scales, determining for each coarse scale a set of posterior probabilities. The posterior oil a coarse scale is used Lis the prior for activity at the next finer scale. We have applied our method both to real as well as synthetic data of block experiments. A linear model and a standard hemodynamic response function are used to construct the likelihood. ROC curves are used to compare the results with other Bayesian and orthodox methods. By systematically deleting images in each period or by corrupting the signal with noise. we can Study the robustness of the method under information loss.