Profile-based sensitivity in the design of experiments for parameter precision

Abstract

D-optimal experimental designs for precise parameter estimation are designs which minimize the determinant of the variance-covariance matrix of the parameter estimates based on the conventional parametric sensitivity coefficients. These coefficients are local measures of sensitivity defined by the first-order derivative of system model function with respect to parameters of interest. For nonlinear models, linear sensitivity information fail to gouge the sensitivity behavior of the model and hence, the resulting determinant of variance-covariance matrix may not give a true indication of the volume of the joint inference region for system parameters. In this article, we employ the profile-based sensitivity coefficients developed by Sulieman et.al. (2001, 2004)in the D-optimal experimental designs. Profile-based sensitivity coefficients account for both model nonlinearity and parameter estimate correlations and are, therefore, expected to yield better precision of parameter estimates when used in the optimization of particular experimental design criteria. Some characteristics of the profile-based designs and related computational aspects are discussed. Application of the new designs to nonlinear model case is also presented.