  M/EEG source localization is an open research issue. To solve it, it is
important to have good knowledge of several physical parameters to build a
reliable head operator. Amongst them, the value of the conductivity of the
human skull has remained controversial. This report introduces a novel
hierarchical Bayesian framework to estimate the skull conductivity jointly with
the brain activity from the M/EEG measurements to improve the reconstruction
quality. A partially collapsed Gibbs sampler is used to draw samples
asymptotically distributed according to the associated posterior. The generated
samples are then used to estimate the brain activity and the model
hyperparameters jointly in a completely unsupervised framework. We use
synthetic and real data to illustrate the improvement of the reconstruction.
The performance of our method is also compared with two optimization algorithms
introduced by Vallagh\'e \textit{et al.} and Gutierrez \textit{et al.}
respectively, showing that our method is able to provide results of similar or
better quality while remaining applicable in a wider array of situations.
