Skip to main content
SpringerLink
Log in

Discussion of parameter estimation in biological modelling: Algorithms for estimation and evaluation of the estimates

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Summary

This paper is concerned with the estimation of parameters when mathematical models are fitted to data. Two new algorithms are presented. The first is fast (economical in computation time), requires no initial estimates, but is not so accurate. The second requires more computation time, and fairly accurate initial estimates, but achieves high accuracy. The models discussed consist of sets of coupled, non-linear differential equations, but the second algorithm is applicable to wider classes of models as well.

The accuracy of the computed values of the parameters depends on the number of data points, and the errors in the data. The sensitivity of the different parameters to errors may differ by orders of magnitude. A method of calculating the expected errors in the parameters is described, and the results of some applications of the method are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Rosenbrock, H., Storey, C.: Computational Techniques for Chemical Engineers. Oxford: Pergamon Press 1966.

    Google Scholar 

  2. Davis, R., Ottaway, J.: Applications of optimization procedures to tracer kinetic data. Math. Bios. I.13, 265 (1972).

    Article  Google Scholar 

  3. Swann, W. H.: A survey of non-linear optimization techniques. F. E. B. S. Letters2, 539 (1969).

    Article  Google Scholar 

  4. Himmelblau, D. M., et al.: Determination of Rate constants for complex kinetic models. Ind. Eng. Chem. Fundam.6, 539 (1967).

    Article  Google Scholar 

  5. Swartz, J.: Parameter estimation in biological systems. Ph. D. Thesis, University of California, Berkeley, 1973.

    Google Scholar 

  6. Chandler, J., et al.: A program for efficient integration of rate equations and least-squares fitting of chemical reaction data. Comput. Biomed. Res.5, 515 (1972).

    Article  Google Scholar 

  7. Squire, W.: A simple integral method for system identification. Math. Biosi.10, 145 (1971).

    Article  Google Scholar 

  8. Ralston, A.: A First Course in Numerical Analysis. New York: McGraw-Hill 1965.

    MATH  Google Scholar 

  9. Bremermann, H.: A method of unconstrained global optimization. Math. Biosi.9, 1 (1970).

    Article  MathSciNet  MATH  Google Scholar 

  10. Bellman, R., et al.: Inverse problems in ecology. J. Theoret. Biol.11, 164 (1966).

    Article  Google Scholar 

  11. Garfinkel, D.: A simulation study of the effect on simple ecological systems of making rate of increase of population density-dependent. J. Theoret. Biol.14, 46 (1967).

    Article  Google Scholar 

  12. Roth, R., Roth, M.: Data unscrambling and the analysis of inducible enzyme synthesis. Math. Biosi.5, 57 (1969).

    Article  Google Scholar 

  13. Lanczos, C.: Applied Analysis. Englewood Cliffs, N.J.: Prentice-Hall 1956.

    MATH  Google Scholar 

  14. Vandermeer, J.: The competitive structure of communities: an experimental approach with protozoa. Ecology50, 362 (1970).

    Article  Google Scholar 

  15. Gause, G.: The Struggle for Existence. New York: Hafner 1934, reprinted 1964.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Public Health Environmental Health Sciences, University of California, 94720, Berkeley, CA, USA

    J. Swartz

  2. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    H. Bremermann

Authors
  1. J. Swartz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Bremermann
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This investigation was supported in part by USPHS Training Grant No. 2-T01-GM 00829 from the National Institute of General Medical Sciences.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Swartz, J., Bremermann, H. Discussion of parameter estimation in biological modelling: Algorithms for estimation and evaluation of the estimates. J. Math. Biology 1, 241–257 (1975). https://doi.org/10.1007/BF01273746

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01273746

Keywords

Search

Navigation