Open Access
June 2014 A statistical approach to the inverse problem in magnetoencephalography
Zhigang Yao, William F. Eddy
Ann. Appl. Stat. 8(2): 1119-1144 (June 2014). DOI: 10.1214/14-AOAS716


Magnetoencephalography (MEG) is an imaging technique used to measure the magnetic field outside the human head produced by the electrical activity inside the brain. The MEG inverse problem, identifying the location of the electrical sources from the magnetic signal measurements, is ill-posed, that is, there are an infinite number of mathematically correct solutions. Common source localization methods assume the source does not vary with time and do not provide estimates of the variability of the fitted model. Here, we reformulate the MEG inverse problem by considering time-varying locations for the sources and their electrical moments and we model their time evolution using a state space model. Based on our predictive model, we investigate the inverse problem by finding the posterior source distribution given the multiple channels of observations at each time rather than fitting fixed source parameters. Our new model is more realistic than common models and allows us to estimate the variation of the strength, orientation and position. We propose two new Monte Carlo methods based on sequential importance sampling. Unlike the usual MCMC sampling scheme, our new methods work in this situation without needing to tune a high-dimensional transition kernel which has a very high cost. The dimensionality of the unknown parameters is extremely large and the size of the data is even larger. We use Parallel Virtual Machine (PVM) to speed up the computation.


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Zhigang Yao. William F. Eddy. "A statistical approach to the inverse problem in magnetoencephalography." Ann. Appl. Stat. 8 (2) 1119 - 1144, June 2014.


Published: June 2014
First available in Project Euclid: 1 July 2014

zbMATH: 06333790
MathSciNet: MR3262548
Digital Object Identifier: 10.1214/14-AOAS716

Keywords: Ill-posed problem , parallel computing , sequential importance sampling , source localization , state space model

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.8 • No. 2 • June 2014
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