A Bayesian test for the appropriateness of a model in the biomagnetic inverse problem

This paper extends previous work on the Bayesian foundations of the biomagnetic inverse problem. It derives the a posteriori source current probability distribution given a prior source current probability distribution, a source space weight function and a data set. This calculation enables the construction of a Bayesian test for the appropriateness of any a priori choice of source distribution including the optimal distribution associated with any specific model. In this way the adequacy of a model may be tested. The procedure is as follows. A model for the sources is chosen, e.g. a single equivalent current dipole. The method then produces a map in source space of the probability that the data imply a significant difference between the real distribution and that associated with the model. The procedure is illustrated using both simulated data generated by a multi-dipolar source set and the results of a study of early latency processing of images of human faces.