Optimal design for parameter estimation in EEG problems in a 3D multilayered domain
The fundamental problem of collecting data in the ``best way'' in order to assure statistically efficient estimation of parameters is known as Optimal Experimental Design. Many inverse problems consist in selecting best parameter values of a given mathematical model based on fits to measu...
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| Format: | Article |
| Language: | English |
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AIMS Press
2015-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.739 |
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| author | H. T. Banks D. Rubio N. Saintier M. I. Troparevsky |
| author_facet | H. T. Banks D. Rubio N. Saintier M. I. Troparevsky |
| author_sort | H. T. Banks |
| collection | DOAJ |
| description | The fundamental problem of collecting data in the ``best way'' in order to assure statistically efficient estimation of parameters is known as Optimal Experimental Design. Many inverse problems consist in selecting best parameter values of a given mathematical model based on fits to measured data. These are usually formulated as optimization problems and the accuracy of their solutions depends not only on the chosen optimization scheme but also on the given data.We consider an electromagnetic interrogation problem, specifically one arising in an electroencephalography (EEG) problem, of finding optimal number and locations for sensors for source identification in a 3D unit sphere from data on its boundary. In this effort we compare the use of the classical $D$-optimal criterion for observation points as opposed to that for a uniform observation mesh. We consider location and best number of sensors and report results based on statistical uncertainty analysis of the resulting estimated parameters. |
| format | Article |
| id | doaj-art-29746cb3e68b4a16a49be75fe991f793 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-29746cb3e68b4a16a49be75fe991f7932025-01-24T02:32:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-03-0112473976010.3934/mbe.2015.12.739Optimal design for parameter estimation in EEG problems in a 3D multilayered domainH. T. Banks0D. Rubio1N. Saintier2M. I. Troparevsky3Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8212Centro de Matemática Aplicada, Universidad de San Martín, Buenos AiresInstituto de Ciencias, Universidad Nacional Gral. Sarmiento, Buenos AiresDep. de Matemática, Facultad de Ingeniería, Universidad de Buenos AiresThe fundamental problem of collecting data in the ``best way'' in order to assure statistically efficient estimation of parameters is known as Optimal Experimental Design. Many inverse problems consist in selecting best parameter values of a given mathematical model based on fits to measured data. These are usually formulated as optimization problems and the accuracy of their solutions depends not only on the chosen optimization scheme but also on the given data.We consider an electromagnetic interrogation problem, specifically one arising in an electroencephalography (EEG) problem, of finding optimal number and locations for sensors for source identification in a 3D unit sphere from data on its boundary. In this effort we compare the use of the classical $D$-optimal criterion for observation points as opposed to that for a uniform observation mesh. We consider location and best number of sensors and report results based on statistical uncertainty analysis of the resulting estimated parameters.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.739asymptotic error analysis.optimal design in 3d eeg analysisparameter estimationelectromagnetic inverse problems |
| spellingShingle | H. T. Banks D. Rubio N. Saintier M. I. Troparevsky Optimal design for parameter estimation in EEG problems in a 3D multilayered domain Mathematical Biosciences and Engineering asymptotic error analysis. optimal design in 3d eeg analysis parameter estimation electromagnetic inverse problems |
| title | Optimal design for parameter estimation in EEG problems in a 3D multilayered domain |
| title_full | Optimal design for parameter estimation in EEG problems in a 3D multilayered domain |
| title_fullStr | Optimal design for parameter estimation in EEG problems in a 3D multilayered domain |
| title_full_unstemmed | Optimal design for parameter estimation in EEG problems in a 3D multilayered domain |
| title_short | Optimal design for parameter estimation in EEG problems in a 3D multilayered domain |
| title_sort | optimal design for parameter estimation in eeg problems in a 3d multilayered domain |
| topic | asymptotic error analysis. optimal design in 3d eeg analysis parameter estimation electromagnetic inverse problems |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.739 |
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