Abstract:  The talk is devoted to constructing and studying optimal experimental designs for regression models used in microbiology. We consider nonlinear in parameters regression models, particularly, Michaelis-Menten and Monod models (see Dette et al., 2003 for explanations on optimal design for the Monod model). It is known that the asymptotic covariance matrix for such models depends on proper values of the parameters. There exist three known ways (locally optimal, maximin and Bayesian) to overcome this difficulty. For the first two in the recent book (Melas, 2006) a functional approach was developed. It consists of expanding the optimal design points into Taylor series in some parameters. In this talk we will give a review of corresponding results and their development for Bayesian outline. We will show that the Bayesian optimal designs are more efficient in most cases as compared with popular alternative designs (equidistant, locally optimal and maximin efficient).



References: 

H. Dette, V.Melas, A. Pepelyshev, and N. Strigul (2003). Efficient design of experiments in the Monod model. Journal of Royal Statistical Society, ser. B, 65, Part 3, 725-742.

Melas, V.B. (2006). Functional approach to optimal experimental design. Lecture Notes in Statistics, vol. 184. New York, Springer.