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Sato, 2001). The resulting algorithm is an iterative procedure that converges quickly because the VB algorithm is a type of natural gradient method (Amari, 1998) that has an optimal local convergence property. The VB method also provides a model selection criterion and is used to select the most probable surface on which the source current is located when there is no prior information on the source position. This paper presents principles and performance of the new hierarchical Bayesian method in comparison with the conventional linear inverse methods for the three different situations: (1) MEG with no other data, (2) MEG with structural MRI data on cortical surfaces, and (3) MEG with both structural MRI and fMRI data. We also examined the performance of our method and the Wiener filter method for incorrect fMRI information. Methods Bayesian and linear filter approaches for MEG inverse problem When neural current activity occurs in the brain, it produces a magnetic field observed by MEG. The relationship between the magnetic field B = {Bmjm = 1:M}1 measured by M sensors and the primary source current J = { Jnjn = 1:N} in the brain is given by B ? G d J;

?1? where G = { Gm,njm =........