Computational modelling with functional differential equations: Identification, selection, and sensitivity

Hdl Handle:
http://hdl.handle.net/10034/67654
Title:
Computational modelling with functional differential equations: Identification, selection, and sensitivity
Authors:
Baker, Christopher T. H.; Bocharov, Gennady; Paul, C. A. H.; Rihan, F. A. R.
Abstract:
Mathematical models based upon certain types of differential equations, functional differential equations, or systems of such equations, are often employed to represent the dynamics of natural, in particular biological, phenomena. We present some of the principles underlying the choice of a methodology (based on observational data) for the computational identification of, and discrimination between, quantitatively consistent models, using scientifically meaningful parameters. We propose that a computational approach is essential for obtaining meaningful models. For example, it permits the choice of realistic models incorporating a time-lag which is entirely natural from the scientific perspective. The time-lag is a feature that can permit a close reconciliation between models incorporating computed parameter values and observations. Exploiting the link between information theory, maximum likelihood, and weighted least squares, and with distributional assumptions on the data errors, we may construct an appropriate objective function to be minimized computationally. The minimizer is sought over a set of parameters (which may include the time-lag) that define the model. Each evaluation of the objective function requires the computational solution of the parametrized equations defining the model. To select a parametrized model, from amongst a family or hierarchy of possible best-fit models, we are able to employ certain indicators based on information-theoretic criteria. We can evaluate confidence intervals for the parameters, and a sensitivity analysis provides an expression for an information matrix, and feedback on the covariances of the parameters in relation to the best fit. This gives a firm basis for any simplification of the model (e.g., by omitting a parameter).
Affiliation:
University College Chester ; Institute of Numerical Mathematics, Russian Academy of Sciences ; University of Salford
Citation:
Applied Numerical Mathematics, 2005, 53(2-4), pp. 107-129
Publisher:
Elsevier
Journal:
Applied Numerical Mathematics
Publication Date:
2005
URI:
http://hdl.handle.net/10034/67654
DOI:
10.1016/j.apnum.2004.08.014
Additional Links:
http://www.sciencedirect.com/science/journal/01689274
Type:
Article
Language:
en
Description:
This article is not available through ChesterRep
ISSN:
0168-9274
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorBaker, Christopher T. H.en
dc.contributor.authorBocharov, Gennadyen
dc.contributor.authorPaul, C. A. H.en
dc.contributor.authorRihan, F. A. R.en
dc.date.accessioned2009-05-08T11:14:35Zen
dc.date.available2009-05-08T11:14:35Zen
dc.date.issued2005en
dc.identifier.citationApplied Numerical Mathematics, 2005, 53(2-4), pp. 107-129en
dc.identifier.issn0168-9274en
dc.identifier.doi10.1016/j.apnum.2004.08.014en
dc.identifier.urihttp://hdl.handle.net/10034/67654en
dc.descriptionThis article is not available through ChesterRepen
dc.description.abstractMathematical models based upon certain types of differential equations, functional differential equations, or systems of such equations, are often employed to represent the dynamics of natural, in particular biological, phenomena. We present some of the principles underlying the choice of a methodology (based on observational data) for the computational identification of, and discrimination between, quantitatively consistent models, using scientifically meaningful parameters. We propose that a computational approach is essential for obtaining meaningful models. For example, it permits the choice of realistic models incorporating a time-lag which is entirely natural from the scientific perspective. The time-lag is a feature that can permit a close reconciliation between models incorporating computed parameter values and observations. Exploiting the link between information theory, maximum likelihood, and weighted least squares, and with distributional assumptions on the data errors, we may construct an appropriate objective function to be minimized computationally. The minimizer is sought over a set of parameters (which may include the time-lag) that define the model. Each evaluation of the objective function requires the computational solution of the parametrized equations defining the model. To select a parametrized model, from amongst a family or hierarchy of possible best-fit models, we are able to employ certain indicators based on information-theoretic criteria. We can evaluate confidence intervals for the parameters, and a sensitivity analysis provides an expression for an information matrix, and feedback on the covariances of the parameters in relation to the best fit. This gives a firm basis for any simplification of the model (e.g., by omitting a parameter).en
dc.language.isoenen
dc.publisherElsevieren
dc.relation.urlhttp://www.sciencedirect.com/science/journal/01689274en
dc.subjectcomputationen
dc.subjectdifferential equationsen
dc.subjectidentifiabilityen
dc.subjectmodellingen
dc.titleComputational modelling with functional differential equations: Identification, selection, and sensitivityen
dc.typeArticleen
dc.contributor.departmentUniversity College Chester ; Institute of Numerical Mathematics, Russian Academy of Sciences ; University of Salforden
dc.identifier.journalApplied Numerical Mathematicsen
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