  We present a new approach to the electromagnetic inverse problem that
explicitly addresses the ambiguity associated with its ill-posed character.
Rather than calculating a single ``best'' solution according to some criterion,
our approach produces a large number of likely solutions that both fit the data
and any prior information that is used. While the range of the different likely
results is representative of the ambiguity in the inverse problem even with
prior information present, features that are common across a large number of
the different solutions can be identified and are associated with a high degree
of probability. This approach is implemented and quantified within the
formalism of Bayesian inference which combines prior information with that from
measurement in a common framework using a single measure. To demonstrate this
approach, a general neural activation model is constructed that includes a
variable number of extended regions of activation and can incorporate a great
deal of prior information on neural current such as information on location,
orientation, strength and spatial smoothness. Taken together, this activation
model and the Bayesian inferential approach yield estimates of the probability
distributions for the number, location, and extent of active regions. Both
simulated MEG data and data from a visual evoked response experiment are used
to demonstrate the capabilities of this approach.
