Bayesian inference in the uncertain EEG problem including local information and a sensor correlation matrix

We present a framework based on Bayesian inference to combine expert judgment and the problem of an uncertain conductivity in the electroencephalography (EEG) inverse problem. A three layer spherical head model with different and random layer conductivities is considered. The randomness is modeled by Legendre Polynomial Chaos. Using this Polynomial Chaos we build on previous work to obtain a correlation matrix for the error used in the likelihood function of the Bayesian procedure. We compare with a classical isotropic correlation.