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  • 1
    Electronic Resource
    Electronic Resource
    Statistical methods for model comparison in parameter estimation problems for distributed systems (1990)
    Springer
    Journal of mathematical biology 28 (1990), S. 501-527 
    Details
    ISSN: 1432-1416
    Keywords: Hypothesis testing ; Parameter estimation ; Partial differential equations ; Approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this note we outline some recent results on the development of a statistical testing methodology for inverse problems involving partial differential equation models. Applications to several problems from biology are presented. The statistical tests, which are in the spirit of analysis of variance (ANOVA), are based on asymptotic distributional results for estimators and residuals in a least squares approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00164161
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Estimation of growth and survival in size-structured cohort data: an application to larval striped bass (Morone saxatilis) (1991)
    Springer
    Journal of mathematical biology 30 (1991), S. 125-150 
    Details
    ISSN: 1432-1416
    Keywords: Size-structural population models ; Parameter estimation ; Growth and mortality rates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We present a method for estimating growth and mortality rates in size-structured population models. The methods are based on least-square fits to data using approximate models (using spline approximations) for the underlying partial differential equation population model. In a series of numerical tests, we compare our approach to an existing method (due to Hackney and Webb). As an example, we apply our techniques to experimental data from larval striped bass field studies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00160331
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Parameter estimation techniques for transport equations with application to population dispersal and tissue bulk flow models (1983)
    Springer
    Journal of mathematical biology 17 (1983), S. 253-273 
    Details
    ISSN: 1432-1416
    Keywords: Parameter estimation ; Transport in tissue ; Insect dispersal ; Spline approximations ; Parabolic equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We develop techniques for estimating the coefficients, boundary data, and initial data associated with transport equations (or more generally, parabolic distributed models). Our estimation schemes are based on cubic spline approximations, for which convergence results are given. We discuss the performance of these techniques in two investigations of biological interest: (1) transport of labeled sucrose in brain tissue white matter, (2) insect dispersal that cannot be modeled by a random diffusion mechanism alone.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276516
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Parameter estimation techniques for interaction and redistribution models: a predator-prey example (1987)
    Springer
    Oecologia 74 (1987), S. 356-362 
    Details
    ISSN: 1432-1939
    Keywords: Parameter estimation ; Species interaction ; redistribution ; Heterogeneous environments
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary The use of parameter estimation techniques for partial differential equations is illustrated using a predatorprey model. Whereas ecologists have often estimated parameters in models, they have not previously been able to do so for models that describe interactions in heterogeneous environments. The techniques we describe for partial differential equations will be generally useful for models of interacting species in spatially complex environments and for models that include the movement of organisms. We demonstrate our methods using field data from a ladybird beetle (Coccinella septempunctata) and aphid (Uroleucon nigrotuberculatum) interaction. Our parameter estimation algorithms can be employed to identify models that explain better than 80% of the observed variance in aphid and ladybird densities. Such parameter estimation techniques can bridge the gap between detail-rich experimental studies and abstract mathematical models. By relating the particular bestfit models identified from our experimental data to other information on Coccinella behavior, we conclude that a term describing local taxis of ladybirds towards prey (aphids in this case) is needed in the model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00378930
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    Paper (German National Licenses)
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