Nonlinearity, Scale, and Sensitivity for Parameter Estimation Problems

Uncertainty assessment for parameter estimation problems is considered. It is customary to use confidence regions or intervals to give the precision of the parameter estimates. The method most used, because of modest computational requirements, is linearized covariance analysis. Monte Carlo analysis can be used to check the validity of the linearization for a particular model, but is clearly not practical as a standard procedure. Curvature measures of nonlinearity have been suggested as a diagnostic tool to help decide when the linearized analysis is applicable. For an ODE model, a correlation between high nonlinearity, low sensitivity, and small-scale perturbations, has been reported. Recently, the existence of such a correlation for a large class of nonlinear models, including the ODE model, was found. Here, we utilize this correlation within assessment of parameter uncertainty. It is shown that care must be exercised when Address all correspondence to this author. †Now with RF-Rogaland Research, Thormøhlensgt. 55, N-5008 Bergen, Norway, Email: [email protected] applying nonlinearity measures as a diagnostic tool for the validity of linearized covariance analysis. For models within the class where the correlation applies, a modified version of the nonlinearity measures may be preferable for this purpose.