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In the present paper, we develop a novel Bayesian approach to the problem ofestimating neural currents in the brain from a fixed distribution of magneticfield (called \emph{topography}), measured by magnetoencephalography.Differently from recent studies that describe inversion techniques, such asspatio-temporal regularization/filtering, in which neural dynamics always playsa role, we face here a purely static inverse problem. Neural currents aremodelled as an unknown number of current dipoles, whose state space isdescribed in terms of a variable--dimension model. Within the resultingBayesian framework, we set up a sequential Monte Carlo sampler to explore theposterior distribution. An adaptation technique is employed in order toeffectively balance the computational cost and the quality of the sampleapproximation. Then, both the number and the parameters of the unknown currentdipoles are simultaneously estimated. The performance of the method is assessedby means of synthetic data, generated by source configurations containing up tofour dipoles. Eventually, we describe the results obtained by analyzing datafrom a real experiment, involving somatosensory evoked fields, and compare themto those provided by three other methods.

Bayesian Multi--Dipole Modeling of a Single Topography in MEG by Adaptive Sequential Monte Carlo Samplers