Controlling the error in FMRI: Hypothesis testing or set estimation?

This paper describes a new methodology and associated theoretical analysis for rapid and accurate extraction of activation regions from functional MRI data. Most fMRI data analysis methods in use today adopt a hypothesis testing approach, in which the BOLD signals in individual voxels or clusters of voxels are compared to a threshold. In order to obtain statistically meaningful results, the testing must be limited to very small numbers of voxels/clusters or the threshold must be set extremely high. Furthermore, voxelization introduces partial volume effects (PVE), which present a persistent error in the localization of activity that no testing procedure can overcome. We abandon the multiple hypothesis testing approach in this paper, and instead advocate a new approach based on set estimation. Rather then attempting to control the probability of error, our method aims to control the spatial volume of the error. To do this, we view the activation regions as level sets of the statistical parametric map (SPM) under consideration. The estimation of the level sets, in the presence of noise, is then treated as a statistical inference problem. We propose a level set estimator and show that the expected volume of the error is proportional to the sidelength of a voxel. Since PVEs are unavoidable and produce errors of the same order, this is the smallest error volume achievable. Experiments demonstrate the advantages of this new theory and methodology, and the statistical reasonability of controlling the volume of the error rather than the probability of error.