Abstract
Testing parametric models for identifiability is particularly important for knowledge-based models. If several values of the parameter vector lead to the same observed behavior, then one may try to modify the experimental set-up to eliminate this ambiguity (which corresponds to performing qualitative experiment design). The tediousness of the algebraic operations involved in such tests makes computer algebra particularly attractive. This paper describes some limitations of this classical approach and explores an alternative route based on new definitions of identifiability and numerical tests implemented in a guaranteed way. The new approach is illustrated in the context of compartmental modeling, widely used in biology.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Norton, J.P.: An Introduction to Identification. Academic Press, London (1986)
Ljung, L.: System Identification, Theory for the User, 2nd edn. Prentice Hall, Englewood Cliffs (1999)
Walter, E., Pronzato, L.: Identification of Parametric Models from Experimental Data. Springer, London (1997)
Jacquez, J.A.: Compartmental Analysis in Biology and Medecine. Elsevier, Amsterdam (1972)
Godfrey, K.: Compartimental Models and Their Application. Academic Press, London (1983)
Walter, E.: Identifiability of State Space Models. Springer, Berlin (1982)
Raksanyi, A., Lecourtier, Y., Walter, E., Venot, E.: Identifiability and distinguishability testing in computer algebra. Math. Biosci. 77(1-2), 245–266 (1985)
Braems, I., Jaulin, L., Kieffer, M., Walter, E.: Guaranteed numerical alternatives to structural identifiability testing. In: Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, pp. 3122–3128 (2001)
Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis. Springer, London (2001)
Balant, L.: Applicability of different types of models in health and disease. Drug Metab. Rev. 15, 75–102 (1984)
Venot, A., Walter, E., Lecourtier, Y., Raksanyi, A., Chauvelot-Moachon, L.: Structural identifiability of ”first-pass” models. Journal of Pharmacokinetics and Biopharmaceutics 15, 179–189 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Walter, E., Braems, I., Jaulin, L., Kieffer, M. (2004). Guaranteed Numerical Computation as an Alternative to Computer Algebra for Testing Models for Identifiability. In: Alt, R., Frommer, A., Kearfott, R.B., Luther, W. (eds) Numerical Software with Result Verification. Lecture Notes in Computer Science, vol 2991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24738-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-24738-8_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21260-7
Online ISBN: 978-3-540-24738-8
eBook Packages: Springer Book Archive