Planning Herbicide Dose-Response Bioassays Using the Bootstrap

  • Silvio Sandoval Zocchi
  • Clarice Garcia Borges Demétrio
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 51)


Dose response herbicide bioassays generally demand large amounts of time and resources. The choice of doses to be used is thus critical. For a given model, optimum design theory can be used to generate optimum designs for parameter estimation. However, such designs depend on the parameter values and in general do not have enough support points to detect lack of fit. This work describes the use of bootstrap methods to generate an empirical distribution of the optimum design points, based on the results of a previous experiment, and suggests designs based on this distribution. These designs are then compared to the Bayesian D-optimum designs


D-optimum designs Bayesian D-optimum designs Bootstrap Non-linear models Dose-response models 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Atkinson, A.C. and Donev, A.N. (1992). Optimum Experimental Designs. Oxford: Oxford University Press.zbMATHGoogle Scholar
  2. Chaloner, K. and Verdinelli, I. (1995). Bayesian experimental design: a review. Stat. Sci. 10, 273–304.MathSciNetzbMATHCrossRefGoogle Scholar
  3. Davison, A.C. and Hinkley, D.V. (1997). Bootstrap Methods and Their Application. Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  4. Efron, B. and Tibshirani, R.J. (1993). An Introduction to the Bootstrap. London: Chapman & Hall.zbMATHGoogle Scholar
  5. Fedorov, V.V. (1972). Theory of Optimal Experiments. London: Academic Press.Google Scholar
  6. Kiefer, J. (1959). Optimum experimental designs (with discussion). J. R. Stat. Soc. B 12, 363–66.MathSciNetGoogle Scholar
  7. Pàzman, A. (1986). Foundations of Optimum Experimental Design. Bratislava: VEDA.zbMATHGoogle Scholar
  8. Powles, S.B. and Holtum, J.A.M. (Eds) (1994). Herbicide Resistance in Plants: Biology and Biochemistry. Boca Raton: Lewis.Google Scholar
  9. Pukelsheim, F. (1993). Optimal Design of Experiments. New York: Wiley.zbMATHGoogle Scholar
  10. Seber, G.A.F. and Wild, C.J. (1989). Nonlinear Regression. New York: Wiley.zbMATHCrossRefGoogle Scholar
  11. Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis. London: Chapman & Hall.zbMATHGoogle Scholar
  12. Silvey, S.D. (1980). Optimal Design. London: Chapman & Hall.zbMATHCrossRefGoogle Scholar
  13. Souza, G.S. (1998). Intwdução aos Modelos de Regressão Linear e Não-linear. Brasília: Embrapa.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Silvio Sandoval Zocchi
    • 1
  • Clarice Garcia Borges Demétrio
    • 1
  1. 1.Departamento de Ciências Exatas, ESALQUniversity of São PauloPiracicabaBrazil

Personalised recommendations