A robust method for nonlinear parameter estimation illustrated on a toxicological model Original Research Article

The paper describes a random search method to estimate both optimal (best-fitting, maximum likelihood) values for the parameters in a nonlinear model and a measure of their uncertainty. The algorithm is robust in the sense that it is relatively insensitive to local minima. In addition, after convergence it returns with a sample of points that directly characterizes the parameter uncertainty, i.e. it is not necessary to make distributional assumptions about the parameters a priori. The method is illustrated on a physiologically realistic toxicological model. This model has a number of properties typical for such models: a nonlinear likelihood function with local maxima and a non-Normal parameter uncertainty.