Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple Delays
This article presents statistical inference methodology based on maximum likelihoods for delay differential equation models in the univariate setting. Maximum likelihood inference is obtained for single and multiple unknown delay parameters as well as other parameters of interest that govern the tra...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2017/6148934 |
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| author | Ahmed A. Mahmoud Sarat C. Dass Mohana S. Muthuvalu Vijanth S. Asirvadam |
| author_facet | Ahmed A. Mahmoud Sarat C. Dass Mohana S. Muthuvalu Vijanth S. Asirvadam |
| author_sort | Ahmed A. Mahmoud |
| collection | DOAJ |
| description | This article presents statistical inference methodology based on maximum likelihoods for delay differential equation models in the univariate setting. Maximum likelihood inference is obtained for single and multiple unknown delay parameters as well as other parameters of interest that govern the trajectories of the delay differential equation models. The maximum likelihood estimator is obtained based on adaptive grid and Newton-Raphson algorithms. Our methodology estimates correctly the delay parameters as well as other unknown parameters (such as the initial starting values) of the dynamical system based on simulation data. We also develop methodology to compute the information matrix and confidence intervals for all unknown parameters based on the likelihood inferential framework. We present three illustrative examples related to biological systems. The computations have been carried out with help of mathematical software: MATLAB® 8.0 R2014b. |
| format | Article |
| id | doaj-art-a1c7471a8dbb483b9c63756a1df76205 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-a1c7471a8dbb483b9c63756a1df762052025-02-03T01:12:26ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/61489346148934Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple DelaysAhmed A. Mahmoud0Sarat C. Dass1Mohana S. Muthuvalu2Vijanth S. Asirvadam3Fundamental and Applied Sciences Department, Faculty of Science and Information Technology, Universiti Teknologi PETRONAS, 32610 Seri Iskandar, Perak, MalaysiaFundamental and Applied Sciences Department, Faculty of Science and Information Technology, Universiti Teknologi PETRONAS, 32610 Seri Iskandar, Perak, MalaysiaFundamental and Applied Sciences Department, Faculty of Science and Information Technology, Universiti Teknologi PETRONAS, 32610 Seri Iskandar, Perak, MalaysiaDepartment of Electrical and Electronic Engineering, Center for Intelligent Signal and Imaging Research (CISIR), Universiti Teknologi PETRONAS, 32610 Seri Iskandar, Perak, MalaysiaThis article presents statistical inference methodology based on maximum likelihoods for delay differential equation models in the univariate setting. Maximum likelihood inference is obtained for single and multiple unknown delay parameters as well as other parameters of interest that govern the trajectories of the delay differential equation models. The maximum likelihood estimator is obtained based on adaptive grid and Newton-Raphson algorithms. Our methodology estimates correctly the delay parameters as well as other unknown parameters (such as the initial starting values) of the dynamical system based on simulation data. We also develop methodology to compute the information matrix and confidence intervals for all unknown parameters based on the likelihood inferential framework. We present three illustrative examples related to biological systems. The computations have been carried out with help of mathematical software: MATLAB® 8.0 R2014b.http://dx.doi.org/10.1155/2017/6148934 |
| spellingShingle | Ahmed A. Mahmoud Sarat C. Dass Mohana S. Muthuvalu Vijanth S. Asirvadam Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple Delays Complexity |
| title | Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple Delays |
| title_full | Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple Delays |
| title_fullStr | Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple Delays |
| title_full_unstemmed | Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple Delays |
| title_short | Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple Delays |
| title_sort | maximum likelihood inference for univariate delay differential equation models with multiple delays |
| url | http://dx.doi.org/10.1155/2017/6148934 |
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