Emergent approaches for model selection
While there is a long tradition of considering inverse modeling as an optimization problem – i.e. designate the solution to an inverse problem as the source model corresponding to the putative global maximum of some adequacy functional – there are situations where, for empirical and/or theoretical reasons, the number of possible solutions is just too large to ensure this goal can be reached. This kind of situations calls for a paradigm shift in the approach to inverse modeling, which animates vivid discussions in the concerned scientific communities (Tarantola, 2006).
In MEG and EEG more specifically, we have admitted that picking a number of dipoles for localization purposes or an imaging prior to insure uniqueness of the solution has its (large) share of arbitrariness. Just like non parametric statistical methods have benefited from the tremendous increase of cheap computational power, Monte-Carlo simulation methods are powerful computational numerical approaches to the general problem of model selection.
Indeed, a relevant question would be to let the data help the researcher decide whether any element from a general class of models would properly account for the data, with possibly predefined confidence intervals on the admissible model parameters.
These approaches are currently emerging from the MEG/EEG literature and have considerable potential (David et al.., 2006, Mattout et al.., 2006, Daunizeau et al.., 2006). It is likely however that the critical ill-posedness of the source modeling problem be detrimental to the efficiency of establishing tight bounds on the admissible model parameters. Further, these techniques are still extremely demanding in terms of computational resources.