  Bayesian modeling and analysis of the MEG and EEG modalities provide a
flexible framework for introducing prior information complementary to the
measured data. This prior information is often qualitative in nature, making
the translation of the available information into a computational model a
challenging task. We propose a generalized gamma family of hyperpriors which
allows the impressed currents to be focal and we advocate a fast and efficient
iterative algorithm, the Iterative Alternating Sequential (IAS) algorithm for
computing maximum a posteriori (MAP) estimates. Furthermore, we show that for
particular choices of the scalar parameters specifying the hyperprior, the
algorithm effectively approximates popular regularization strategies such as
the Minimum Current Estimate and the Minimum Support Estimate. The connection
between priorconditioning and adaptive regularization methods is also pointed
out. The posterior densities are explored by means of a Markov Chain Monte
Carlo (MCMC) strategy suitable for this family of hypermodels. The computed
experiments suggest that the known preference of regularization methods for
superficial sources over deep sources is a property of the MAP estimators only,
and that estimation of the posterior mean in the hierarchical model is better
adapted for localizing deep sources.
