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Efficient design of experiments in the Monod model

Author

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  • Holger Dette
  • Viatcheslav B. Melas
  • Andrey Pepelyshev
  • Nikolai Strigul

Abstract

Summary. Estimation and experimental design in a non‐linear regression model that is used in microbiology are studied. The Monod model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, water research, pharmacokinetics and plant physiology. It is proved that least squares estimates are asymptotically unbiased and normally distributed. The asymptotic covariance matrix of the estimator is the basis for the construction of efficient designs of experiments. In particular locally D‐, E‐ and c‐optimal designs are determined and their properties are studied theoretically and by simulation. If certain intervals for the non‐linear parameters can be specified, locally optimal designs can be constructed which are robust with respect to a misspecification of the initial parameters and which allow efficient parameter estimation. Parameter variances can be decreased by a factor of 2 by simply sampling at optimal times during the experiment.

Suggested Citation

  • Holger Dette & Viatcheslav B. Melas & Andrey Pepelyshev & Nikolai Strigul, 2003. "Efficient design of experiments in the Monod model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 725-742, August.
    • Handle: RePEc:bla:jorssb:v:65:y:2003:i:3:p:725-742
    DOI: 10.1111/1467-9868.00412
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    1. Dette, Holger & Viatcheslav, B. Melas & Pepelyshev, Andrey & Strigul, Nikolai, 2002. "Efficient design of experiments in the Monod model," Technical Reports 2002,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    Cited by:

    1. Wong, Weng Kee & Melas, Viatcheslav B. & Dette, Holger, 2004. "Optimal design for goodness-of-fit of the Michaelis-Menten enzyme kinetic function," Technical Reports 2004,24, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Chiara Tommasi & Juan M. Rodríguez-Díaz & Jesús F. López-Fidalgo, 2023. "An equivalence theorem for design optimality with respect to a multi-objective criterion," Statistical Papers, Springer, vol. 64(4), pages 1041-1056, August.
    3. Pepelyshev, Andrey & Melas, Viatcheslav B. & Strigul, Nikolay & Dette, Holger, 2004. "Design of experiments for the Monod model : robust and efficient designs," Technical Reports 2004,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Strigul, Nikolay & Dette, Holger & Melas, Viatcheslav B., 2006. "A practical guide for optimal designs of experiments in the Monod model," Technical Reports 2006,32, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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