Open Access
September 2020 Quantifying time-varying sources in magnetoencephalography—A discrete approach
Zhigang Yao, Zengyan Fan, Masahito Hayashi, William F. Eddy
Ann. Appl. Stat. 14(3): 1379-1408 (September 2020). DOI: 10.1214/19-AOAS1321


We study the distribution of brain source from the most advanced brain imaging technique, Magnetoencephalography (MEG) which measures the magnetic fields outside of the human head produced by the electrical activity inside the brain. Common time-varying source localization methods assume the source current with a time-varying structure and solve the MEG inverse problem by mainly estimating the source moment parameters. These methods use the fact that the magnetic fields linearly depend on the moment parameters of the source and work well under the linear dynamic system. However, magnetic fields are known to be nonlinearly related to the location parameters of the source. The existing work on estimating the time-varying unknown location parameters is limited. We are motivated to investigate the source distribution for the location parameters based on a dynamic framework, where the posterior distribution of the source is computed in a closed form discretely. The new framework allows us not only to directly approximate the posterior distribution of the source current, where sequential sampling methods may suffer from slow convergence due to the large volume of measurement, but also to quantify the source distribution at any time point from the entire set of measurements reflecting the distribution of the source, rather than using only the measurements up to the time point of interest. Both a dynamic procedure and a switch procedure are pro- posed for the new discrete approach, balancing estimation accuracy and computational efficiency when multiple sources are present. In both simulation and real data, we illustrate that the new method is able to provide comprehensive insight into the time evolution of the sources at different stages of the MEG and EEG experiment.


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Zhigang Yao. Zengyan Fan. Masahito Hayashi. William F. Eddy. "Quantifying time-varying sources in magnetoencephalography—A discrete approach." Ann. Appl. Stat. 14 (3) 1379 - 1408, September 2020.


Received: 1 May 2019; Revised: 1 October 2019; Published: September 2020
First available in Project Euclid: 18 September 2020

MathSciNet: MR4152138
Digital Object Identifier: 10.1214/19-AOAS1321

Keywords: discrete posterior distribution , expectation-maximization , MEG inverse problem , source localization , spatiotemporal model

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.14 • No. 3 • September 2020
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