\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Reduction and identification of dynamic models. Simple example: Generic receptor model

Abstract Related Papers Cited by
  • Identification of biological models is often complicated by the fact that the available experimental data from field measurements is noisy or incomplete. Moreover, models may be complex, and contain a large number of correlated parameters. As a result, the parameters are poorly identified by the data, and the reliability of the model predictions is questionable. We consider a general scheme for reduction and identification of dynamic models using two modern approaches, Markov chain Monte Carlo sampling methods together with asymptotic model reduction techniques. The ideas are illustrated using a simple example related to bio-medical applications: a model of a generic receptor. In this paper we want to point out what the researchers working in biological, medical, etc., fields should look for in order to identify such problematic situations in modelling, and how to overcome these problems.
    Mathematics Subject Classification: 37N25, 34E10, 78M34, 94A20.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    Y. Bard, "Nonlinear Parameter Estimation," Academic Press, New York - London, 1974.

    [2]

    A. Gelman and J. Carlin, "Bayesian Data Analysis," $2^{nd}$ edition, Chapman & Hall/CRC, Boca Raton, FL, 2004.

    [3]

    H. Haario, E. Saksman and J. Tamminen, An adaptive metropolis algorithm, Bernoulli, 7 (2001), 223-242.doi: 10.2307/3318737.

    [4]

    H. Haario, M. Laine, A. Mira and E. Saksman, DRAM: Efficient adaptive MCMC, Stat. Comput., 16 (2006), 339-354.doi: 10.1007/s11222-006-9438-0.

    [5]

    H. Haario, L. Kalachev and M. Laine, Reduced Models for Algae Growth, Bull. Math. Biol., 71 (2009), 1626-1648.doi: 10.1007/s11538-009-9417-7.

    [6]

    J. Kevorkian and J. Cole, "Singular Perturbation Methods in Applied Mathematics," Springer-Verlag, Berlin-Heidelberg-New York, 1981.

    [7]

    J. Murray, "Mathematical Biology," $2^{nd}$ edition, Springer-Verlag, Berlin-Heidelberg-New York, 1993.doi: 10.1007/b98869.

    [8]

    R. O'Malley, "Singular Perturbations Methods for Ordinary Differential Equations," Springer-Verlag, Berlin-Heidelberg-New York, 1991.doi: 10.1007/978-1-4612-0977-5.

    [9]

    A. Vasil'eva, V. Butuzov and L. Kalachev, "The Boundary Function Method for Singular Perturbation Problems," SIAM, Philadelphia, PA, 1995.doi: 10.1137/1.9781611970784.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(89) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return