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 (M CMC) methods for solving the magnetoencephalography (MEG) inverse problem, by using an algorithm composed of the combination of two MCMC samplers: Rev ersible 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 bett er resolution of the MEG inverse problem even when the number of source dip oles is unknown (RJ), and significant reduction of the probability of erron eous convergence to local modes (PT), First estimates of the accuracy and r esolution of our composite algorithm are given from results of simulation s tudies obtained with an unknown number of sources, and with white and neuro magnetic noise. In contrast to other approaches, MCMC methods do not just g ive an estimation of a "single best" solution, but they provide confidence interval for the source localization, probability distribution for the numb er of fitted dipoles, and estimation of other almost equally likely solutio ns.