Arbeitspapier
Design of experiments for the Monod model : robust and efficient designs
In this paper the problem of designing experiments for a model which is called Monod model and is frequently used in microbiology is studied. The model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, environmental research, pharmacokinetics, and plant physiology. The designs presented so far in the literature are locally optimal designs, which depend sensitively on a preliminary guess of the unknown parameters, and are for this reason in many cases not robust with respect to their misspecification. Uniform designs and maximin optimal designs are considered as a strategy to obtain robust and efficient designs for parameter estimation. In particular standardized maximin D- and E- optimal designs are determined and compared with uniform designs, which are usually applied in these microbiological models. It is shown that standardized maximin optimal designs are always supported on a finite number of points and it is demonstrated that maximin optimal designs are substantially more efficient than uniform designs. Parameter variances can be decreased by a factor two by simply sampling at optimal times during the experiment. Moreover, the maximin optimal designs usually provide the possibility for the experimenter to check the model assumptions, because they have more support points than parameters in the Monod model.
- Language
-
Englisch
- Bibliographic citation
-
Series: Technical Report ; No. 2004,36
- Subject
-
robust designs
maximin optimal designs
microbial growth
biodegradation kinetics
Monod model
Experiment
Robustes Verfahren
Mathematische Optimierung
Theorie
- Event
-
Geistige Schöpfung
- (who)
-
Pepelyshev, Andrey
Melas, Viatcheslav B.
Strigul, Nikolay
Dette, Holger
- Event
-
Veröffentlichung
- (who)
-
Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen
- (where)
-
Dortmund
- (when)
-
2004
- Handle
- Last update
-
10.03.2025, 11:41 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Arbeitspapier
Associated
- Pepelyshev, Andrey
- Melas, Viatcheslav B.
- Strigul, Nikolay
- Dette, Holger
- Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen
Time of origin
- 2004
Other Objects (12)
On robust and efficient designs for risk estimation in epidemiologic studies
Robust and efficient designs for the Michaelis-Menten model
Efficient design of experiments in the Monod model
Robust designs for series estimation
Efficient experimental designs for sigmoidal growth models
Robust designs for 3D shape analysis with spherical harmonic descriptors
A practical guide for optimal designs of experiments in the Monod model
Efficient experimental design for the Behrens-Fisher problem with application to bioassay
Robust designs for polynomial regression by maximizing a minimum of D- and D1-efficiencies
Optimal discrimination designs
Some robust design strategies for percentile estimation in binary response models
Optimal designs for dose finding studies
On robust and efficient designs for risk estimation in epidemiologic studies
Robust and efficient designs for the Michaelis-Menten model
Efficient design of experiments in the Monod model
Robust designs for series estimation
Efficient experimental designs for sigmoidal growth models
Robust designs for 3D shape analysis with spherical harmonic descriptors
A practical guide for optimal designs of experiments in the Monod model
Efficient experimental design for the Behrens-Fisher problem with application to bioassay
Robust designs for polynomial regression by maximizing a minimum of D- and D1-efficiencies
Optimal discrimination designs
Some robust design strategies for percentile estimation in binary response models
Optimal designs for dose finding studies
On robust and efficient designs for risk estimation in epidemiologic studies
Robust and efficient designs for the Michaelis-Menten model
Efficient design of experiments in the Monod model
Robust designs for series estimation
Efficient experimental designs for sigmoidal growth models
Robust designs for 3D shape analysis with spherical harmonic descriptors
A practical guide for optimal designs of experiments in the Monod model
Efficient experimental design for the Behrens-Fisher problem with application to bioassay
Robust designs for polynomial regression by maximizing a minimum of D- and D1-efficiencies
Optimal discrimination designs
Some robust design strategies for percentile estimation in binary response models