Horwitz's rule, transforming both sides and the design of experiments for mechanistic models

Journal of the Royal Statistical Society. Series C: Applied Statistics

Volumn 52, Issue 3, 2003, Pages 261-278

  Atkinson, Anthony C ^a  

^a LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

Analytical chemistry; Box Cox transformation; Chemical kinetics; D optimum design; Direct method; Model checking; Parameter sensitivities

Indexed keywords

EID: 0038379790     PISSN: 00359254     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9876.00403     Document Type: Article

References (33)

1. Asprey, S. M. and Macchietto, S. (2000) Statistical tools for optimal dynamic model building. Comput. Chem. Engng, 24, 1261-1267.
2. Atkinson, A. C. (1972) Planning experiments to detect inadequate regression models. Biometrika, 59, 275-293.
3. Atkinson, A. C. (2004) Transforming both sides and optimum experimental design for a nonlinear model arising from second-order chemical kinetics. Tatra Mt. Math. Publ., to be published.
4. s-optimum designs for determining the order of a chemical reaction. Technometrics, 39, 347-356.
5. Atkinson, A. C. and Bogacka, B. (2002) Compound and other optimum designs for systems of nonlinear differential equations arising in chemical kinetics. Chemetr. Intell. Lab. Syst., 61, 17-33.
6. Atkinson, A. C., Bogacka, B. and Zocchi, S. (2000) Equivalence theory for design augmentation and parsimonious model checking: response surfaces and yield density models. List. Biometr., 37, 67-95.
7. Atkinson, A. C. and Cook, R. D. (1995) D-optimum designs for heteroscedastic linear models. J. Am. Statist. Ass., 90, 204-212.
8. Atkinson, A. C. and Cook, R. D. (1997) Designing for a response transformation parameter. J. R. Statist. Soc. B, 59, 111-124.
9. Atkinson, A. C. and Donev, A. N. (1992) Optimum Experimental Designs. Oxford: Oxford University Press.
10. Atkinson, A. C. and Riani, M. (2000) Robust Diagnostic Regression Analysis. New York: Springer.
11. Bauer, I., Bock, H. G., Körkel, S. and Schlöder, J. P. (2000) Numerical methods for optimum experimental design in DAE systems. J. Comput. Appl. Math., 120, 1-25.
12. Bogacka, B. and Wright, F. (2003) A non-linear design problem in a chemical kinetic model with non-constant error variance. To be published.
13. Box, G. E. P. and Cox, D. R. (1964) An analysis of transformations (with discussion). J. R. Statist. Soc. B, 26, 211-252.
14. Box, G. E. P. and Hunter, W. G. (1965) Sequential design of experiments for nonlinear models. In Proc. IBM Scientific Computing Symp: Statistics, pp. 113-137. New York: International Business Machines.
15. Box, G. E. P. and Lucas, H. L. (1959) Design of experiments in nonlinear situations. Biometrika, 46, 77-90.
16. Box, M. J. (1971) An experimental design criterion for precise estimation of a subset of the parameters in a nonlinear model. Biometrika, 58, 149-153.
17. Carroll, R. J. and Ruppert, D. (1988) Transformation and Weighting in Regression. London: Chapman and Hall.
18. Chaloner, K. and Larntz, K. (1989) Optimal Bayesian design applied to logistic regression experiments. J. Statist. Planng Inf., 21, 191-208.
19. Chaloner, K. and Verdinelli, I. (1995) Bayesian experimental design: a review. Statist. Sci., 10, 273-304.
20. Downing, D., Fedorov, V. V. and Leonov, S. (2001) Extracting information from the variance function: optimal design. In MODA 6 - Advances in Model-oriented Design and Analysis (eds A. C. Atkinson. P. Hackl and W. G. Müller), pp. 45-52. Heidelberg: Physica.
21. Draper, N. R. and Hunter, W. G. (1966) Design of experiments for parameter estimation in multiresponse situations. Biomelrika, 53, 596-599.
22. DuMouchel, W. and Jones, B. (1994) A simple Bayesian modification of D-optimal designs to reduce dependence on an assumed model. Technometrics, 36, 37-47.
23. Fedorov, V. V. (1972) Theory of Optimal Experiments. New York: Academic Press.
24. Kiefer, J. and Wolfowitz, J. (1960) The equivalence of two extremum problems. Can. J. Math., 12, 363-366.
25. Lindsey, J. K. (2001) Nonlinear Models in Medical Statistics. Oxford: Oxford University Press.
26. Lischer, P. (1999) Good statistical practice in analytical chemistry. In Probability Theory and Mathematical Statistics (ed. B. Grigelionis), pp. 1-12. Zeist: VSP.
27. Mentré, F., Mallet, A. and Baccar, D. (1997) Optimal design in random-effects regression models. Biometrika, 84, 429-442.
28. Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P. (1992) Numerical Recipes in Fortran, 2nd edn. Cambridge: Cambridge University Press.
29. Rocke, D. M. and Lorenzato, S. (1995) A two-component model for measurement error in analytical chemistry. Technometrics, 37, 176-184.
30. Sheiner, L. B. and Beal, S. L. (1980) Evaluation of methods for estimating population pharmacokinetic parameters I, Michaelis-Menten model: routine clinical pharmacokinetic data. J. Pharmkinet. Biopharm., 8, 553-571.
31. Stroud, J. R., Müller, P. and Rosner, G. L. (2001) Optimal sampling times in population pharmacokinetic studies. Appl. Statist., 50, 345-359.
32. Uciński, D. (1999) Measurement Optimization for Parameter Estimation in Distributed Systems. Zielona Góra: Technical University Press.
33. Valko, P. and Vajda, S. (1984) An extended ODE solver for sensitivity calculations. Comput. Chem., 8, 255-271.