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Analysis of Nonlinear Differential Equations: Parameter Estimation and Model Selection

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Book cover Medical Data Analysis (ISMDA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1933))

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Abstract

We have implemented a method for estimating parameters in systems of nonlinear differential equations which is superior to conventional approaches with respect to reliability and effectiveness. The method is based on the multiple shooting approach introduced by Bock (1983). Different models are compared with respect to their adequacy by means of likelihood ratio tests. We demonstrate the advantages of the algorithm with simulated data and present applications from calcium dynamics in skeletal muscle cells and the human lipoprotein metabolism.

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References

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Author information

Authors and Affiliations

  1. Freiburger Zentrum für Datenanalyse und Modellbildung, Eckerstr. 1, D-79104, Freiburg, Germany

    Werner Horbelt, Thorsten Müller & Jens Timmer

  2. Institut für Angewandte Physiologie, Universität Ulm, 89069, Ulm, Germany

    Werner Melzer

  3. Universitätsklinik Freiburg, Germany

    Karl Winkler

Authors
  1. Werner Horbelt
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  2. Thorsten Müller
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  3. Jens Timmer
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  4. Werner Melzer
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  5. Karl Winkler
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Editor information

Editors and Affiliations

  1. Fachbereich Biologie und Informatik AG Adaptive Systemarchitektur, Johann Wolfgang Goethe-Universität, Robert-Mayer-Str. 11-15, 60054, Frankfurt a.M., Germany

    Rüdiger W. Brause

  2. Klinik für Allgemein- und Gefässchirurgie, Johann Wolfgang Goethe-Universität, Theodor-Stern-Kai 7, 60590, Frankfurt a.M., Germany

    Ernst Hanisch

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© 2000 Springer-Verlag Berlin Heidelberg

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Horbelt, W., Müller, T., Timmer, J., Melzer, W., Winkler, K. (2000). Analysis of Nonlinear Differential Equations: Parameter Estimation and Model Selection. In: Brause, R.W., Hanisch, E. (eds) Medical Data Analysis. ISMDA 2000. Lecture Notes in Computer Science, vol 1933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39949-6_19

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  • DOI: https://doi.org/10.1007/3-540-39949-6_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41089-8

  • Online ISBN: 978-3-540-39949-0

  • eBook Packages: Springer Book Archive

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