  We develop a new methodology for determining the location and dynamics of
brain activity from combined magnetoencephalography (MEG) and
electroencephalography (EEG) data. The resulting inverse problem is ill-posed
and is one of the most difficult problems in neuroimaging data analysis. In our
development we propose a solution that combines the data from three different
modalities, MRI, MEG, and EEG, together. We propose a new Bayesian spatial
finite mixture model that builds on the mesostate-space model developed by
Daunizeau and Friston (2007). Our new model incorporates two major extensions:
(i) We combine EEG and MEG data together and formulate a joint model for
dealing with the two modalities simultaneously; (ii) we incorporate the Potts
model to represent the spatial dependence in an allocation process that
partitions the cortical surface into a small number of latent states termed
mesostates. The cortical surface is obtained from MRI. We formulate the new
spatiotemporal model and derive an efficient procedure for simultaneous point
estimation and model selection based on the iterated conditional modes
algorithm combined with local polynomial smoothing. The proposed method results
in a novel estimator for the number of mixture components and is able to select
active brain regions which correspond to active variables in a high-dimensional
dynamic linear model. The methodology is investigated using synthetic data and
simulation studies and then demonstrated on an application examining the neural
response to the perception of scrambled faces. R software implementing the
methodology along with several sample datasets are available at the following
GitHub repository https://github.com/v2south/PottsMix.
