Model selection procedures in electromagnetic source analysis

An essential assumption in estimating the source parameters in electromagnetic source analysis (EMSA) is that the number of sources is known. If the incorrect number of sources is assumed in the estimation procedure, errors could occur [1]. Supek and Aine [2], for example, showed that if too many dipoles are assumed (over-modeling) then ‘spurious’ dipoles could arise with high standard errors, and if too few dipoles are assumed (under-modeling) estimates can be inaccurate but with low standard errors. Given a data set a model selection procedure consists of comparing different models to the data with a model selection criterion (sometimes called goodness of fit function) and then deciding which model is best according to the criterion. Several model selection criteria are available for deciding how many active regions there are in the electroor magnetoencephalogram (EEG/MEG). We consider two types of model selection criteria: regression and likelihood based criteria. In the regression approach the parameters are estimated by least squares (LS) and subsequently inserted in a function derived from the regression function. Likelihood is based on the estimation of parameters by maximum likelihood (ML) and then determining the number of sources with a likelihood ratio type of function. The likelihood case includes the regression case with a specified parametric probability distribution function for the residuals [3]. Regression based criteria are commonly defined for uncorrelated residuals (noise). However, the averaged EEG/MEG noise is correlated (e.g., [4], [5], [6]). To account for the noise correlations the LS function is modified (see e.g., [7]). Consequently, the regression criteria are modified similarly. In the likelihood case noise correlations are accounted for. Many criteria have been examined for linear models. The inverse problem in EMSA is nonlinear, however, and some properties of these criteria are not obviously