A probabilistic solution to the MEG inverse problem via MCMC methods: the reversible jump and parallel tempering algorithms

We investigated the usefulness of probabilistic Markov chain Monte Carlo (MCMC) methods for solving the magnetoencephalography (MEG) inverse problem, by using an algorithm composed of the combination of two MCMC samplers: Reversible Jump (RJ) and Parallel Tempering (PT). The MEG inverse problem was formulated in a probabilistic Bayesian approach, and we describe how the RJ and PT algorithms are fitted to our application. This approach offers better resolution of the MEG inverse problem even when the number of source dipoles is unknown (RJ), and significant reduction of the probability of erroneous convergence to local modes (PT). First estimates of the accuracy and resolution of our composite algorithm are given from results of simulation studies obtained with an unknown number of sources, and with white and neuromagnetic noise. In contrast to other approaches, MCMC methods do not just give an estimation of a "single best" solution, but they provide confidence interval for the source localization, probability distribution for the number of fitted dipoles, and estimation of other almost equally likely solutions.