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Volume 30, Issue 1
Critical Issues in the Numerical Treatment of the Parameter Estimation Problems in Immunology

Tatyana Luzyanina & Gennady Bocharov

DOI: 10.4208/jcm.1110-m11si12

J. Comp. Math., 30 (2012), pp. 59-79.

Published online: 2012-02

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  • Abstract

A robust and reliable parameter estimation is a critical issue for modeling in immunology. We developed a computational methodology for analysis of the best-fit parameter estimates and the information-theoretic assessment of the mathematical models formulated with ODEs. The core element of the methodology is a robust evaluation of the first and second derivatives of the model solution with respect to the model parameter values. The critical issue of the reliable estimation of the derivatives was addressed in the context of inverse problems arising in mathematical immunology. To evaluate the first and second derivatives of the ODE solution with respect to parameters, we implemented the variational equations-, automatic differentiation and complex-step derivative approximation methods. A comprehensive analysis of these approaches to the derivative approximations is presented to understand their advantages and limitations.

  • Keywords

Mathematical modeling in immunology, Parameter estimation, Constrained optimization.

  • AMS Subject Headings

34K29, 92-08, 65K10.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-30-59, author = {Tatyana Luzyanina and Gennady Bocharov}, title = {Critical Issues in the Numerical Treatment of the Parameter Estimation Problems in Immunology}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {1}, pages = {59--79}, abstract = {

A robust and reliable parameter estimation is a critical issue for modeling in immunology. We developed a computational methodology for analysis of the best-fit parameter estimates and the information-theoretic assessment of the mathematical models formulated with ODEs. The core element of the methodology is a robust evaluation of the first and second derivatives of the model solution with respect to the model parameter values. The critical issue of the reliable estimation of the derivatives was addressed in the context of inverse problems arising in mathematical immunology. To evaluate the first and second derivatives of the ODE solution with respect to parameters, we implemented the variational equations-, automatic differentiation and complex-step derivative approximation methods. A comprehensive analysis of these approaches to the derivative approximations is presented to understand their advantages and limitations.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1110-m11si12}, url = {http://global-sci.org/intro/article_detail/jcm/8417.html} }
TY - JOUR T1 - Critical Issues in the Numerical Treatment of the Parameter Estimation Problems in Immunology AU - Tatyana Luzyanina & Gennady Bocharov JO - Journal of Computational Mathematics VL - 1 SP - 59 EP - 79 PY - 2012 DA - 2012/02 SN - 30 DO - http://doi.org/10.4208/jcm.1110-m11si12 UR - https://global-sci.org/intro/article_detail/jcm/8417.html KW - Mathematical modeling in immunology, Parameter estimation, Constrained optimization. AB -

A robust and reliable parameter estimation is a critical issue for modeling in immunology. We developed a computational methodology for analysis of the best-fit parameter estimates and the information-theoretic assessment of the mathematical models formulated with ODEs. The core element of the methodology is a robust evaluation of the first and second derivatives of the model solution with respect to the model parameter values. The critical issue of the reliable estimation of the derivatives was addressed in the context of inverse problems arising in mathematical immunology. To evaluate the first and second derivatives of the ODE solution with respect to parameters, we implemented the variational equations-, automatic differentiation and complex-step derivative approximation methods. A comprehensive analysis of these approaches to the derivative approximations is presented to understand their advantages and limitations.

Tatyana Luzyanina and Gennady Bocharov. (2012). Critical Issues in the Numerical Treatment of the Parameter Estimation Problems in Immunology. Journal of Computational Mathematics. 30 (1). 59-79. doi:10.4208/jcm.1110-m11si12
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