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Estimation of Probability Distributions for Individual Parameters Using Aggregate Population Data

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Stochastic Analysis, Control, Optimization and Applications

Part of the book series: Systems & Control: Foundations & Applications ((SCFA))

Abstract

In this paper we discuss a general methodology for estimating the distribution of individual growth rates in a size-structured population using aggregate population data. The method, for which rigorous theoretical formulations have been developed, is presented in the context of an inverse problem methodology and its use is illustrated with application to mosquitofish, Gambusia affinis, populations in rice fields.

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References

  • Banks, H.T. (1988). In Proceedings IFIP Conference on Optimal Control of Systems Governed by PDE, (Santiago de Compostela, July, 1987) Springer LN in Control and Info. Science, Springer 114, 3–10.

    Google Scholar 

  • Banks, H.T. (1994). In Frontiers of Theoretical Biology, Lecture Notes in Biomathematics, Springer-Verlag, Berlin, 100, 609–623.

    Google Scholar 

  • Banks, H.T., Botsford, L.W., Kappel, F. and Wang, C. (1988). In Proceedings 2nd Course on Mathematical Ecology, (Trieste, December 8-12, 1986), World Press, Singapore, 521–541.

    Google Scholar 

  • Banks, H.T. and Fitzpatrick, B.G. (1991). Quart. Appl. Math 49, 215–235.

    MathSciNet  MATH  Google Scholar 

  • Banks, H.T., Fitzpatrick, B.G. and Zhang, Y. (1996). In Differential Equations and Applications to Biology and to Industry, World Science Press, 13-22.

    Google Scholar 

  • Banks, H.T., Tran, H.T. and Woodward, D.E. (1993). SIAM J. Num. Anal. 30, 1574–1602.

    Article  MathSciNet  MATH  Google Scholar 

  • Botsford, L.W., Vandracek, B., Wainwright, T., Linden, A., Kope, R., Reed, D. and Cech, J.J. (1987). Journal of Mathematical Analysis and Applications, 172, 73–91.

    Google Scholar 

  • Fitzpatrick, B.G. (1993). Journal of Mathematical Analysis and Applications, 172, 73–91.

    Article  MathSciNet  MATH  Google Scholar 

  • Fitzpatrick, B.G. (1994). In Control and Estimated Parameter Systems: Nonlinear Phenomena, Intl. Series in Num. Math., Birkhäuser 118, 131–141.

    MathSciNet  Google Scholar 

  • Fleming, W.H. (1974). In Control Theory, Numerical Methods and Computer Systems Modelling, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, 107, 180–191.

    Google Scholar 

  • Fleming, W.H. (1975). J. Math Biology 2, 219–233.

    Article  MathSciNet  MATH  Google Scholar 

  • Fleming, W.H. and Su, C.H. (1974). Theor. Population Biology 5, 431–449.

    Article  Google Scholar 

  • Harrison, G.W. (1988). Num. Meth. for PDE, 4, 219–232.

    Article  MATH  Google Scholar 

  • Ito, K., Kappel, F. and Peichl, G. (1991). Siam J. Numerical Analysis 28, 923–954.

    Article  MathSciNet  MATH  Google Scholar 

  • Okubo, A. (1980). Diffusion and Ecological Problems: Mathematical Models, Springer-Verlag, New York.

    MATH  Google Scholar 

  • Weiss, G.H. (1968). Bull. Math. Biophys., 30, 427–435.

    Article  MATH  Google Scholar 

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© 1999 Springer Science+Business Media New York

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Banks, H.T., Fitzpatrick, B.G., Potter, L.K., Zhang, Y. (1999). Estimation of Probability Distributions for Individual Parameters Using Aggregate Population Data. In: McEneaney, W.M., Yin, G.G., Zhang, Q. (eds) Stochastic Analysis, Control, Optimization and Applications. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1784-8_21

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  • DOI: https://doi.org/10.1007/978-1-4612-1784-8_21

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7281-6

  • Online ISBN: 978-1-4612-1784-8

  • eBook Packages: Springer Book Archive

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