Bertrand, C. 1, 近江政雄1, 鈴木良次1, 賀戸　久2
1 Human Information System Kanazawa Institute of Technology,
　2 Applied Electronic Laboratory Kanazawa Institute of Technology

　We investigated the usefulness of probabilistic Markov Chain Monte Carlo methods for solving the MEG inverse problem [1], by using a combination of two MCMC samplers : Reversible Jump [2] and Parallel Tempering [3]. We express the MEG inverse problem in a probabilistic Bayesian approach. We describe how the Reversible Jump and Parallel Tempering algorithms are fitted to our context, and what improvements they confer : resolution of the MEG inverse problem even when the number of source dipoles is unknown (Reversible Jump), and significant reduction of the probability of erroneous convergence to local modes (Parallel Tempering). We present results from simulation studies, obtained with an unknown number of sources, and with white and neuromagnetic noise. In contrast to other approaches, MCMC methods doesn’t just give an estimation of a “single best” solution, but provides extremely usefull information such as confidence interval for the source localizations, probability distribution for the number of fitted dipoles, and estimation of other almost equally likely solutions.

[1] D.M. Schmidt, J.S. George, C.C. Wood, “Bayesian inference applied to the electromagnetic inverse problem”, Human Brain Mapping, vol. 7, pp.195-212, 1999.

[2] P.J. Green, “Reversible jump Markov chain Monte Carlo computation and Bayesian model determination”, Biometrika, vol. 82, pp. 711-732, 1995.

[3] C.J. Geyer, “Markov Chain Monte Carlo maximum likelihood”, Computing Science and Statistics : Proceedings of the 23rd Symposium on the Interface,Fairfax : Interface Foundation, ed. E.M. Keramigas, pp. 156-163, 1991.