Practical identifiability of parameters in Monod kinetics and statistical analysis of residuals

A systematic procedure for identifying the number of parameters of a model that can be estimated uniquely by nonlinear regression is presented. The objective function to be minimized is in the form of weighted sum of squares of residuals. The assumptions inherent in the choice of weights and the validity of the parameters estimated are verified by statistical tests. The procedure is illustrated by considering the estimation of parameters for Monod kinetics. Simulated data containing known measurement noise are used initially to illustrate the procedure. Finally, parameters are estimated from different sets of experimental data, and the validity and the uniqueness of the parameters are presented.