Global derivative based sensitivity method for parameter estimation

In nonlinear parameter estimation local sensitivity assessment; conventionally measured by the first-order derivative of the predicted response with respect to a parameter of interest fails to provide a representative picture of the prediction sensitivity in the presence of significant parameter co-dependencies and/or nonlinearities. In this article we derive the profile-based sensitivity measure developed by Sulieman et al. (2001, 2004) [1,2] in the context of model re-parameterization. In particular, the so-called predicted response re-parameterization is shown to ultimately lead to the profile-based sensitivity coefficient defined by the total derivative of the model predicted response with respect to a parameter. Although inherently local, the profile-based measure is shown to handle simultaneous perturbations in parameter values while accounting for their co-dependencies. Thus the proposed measure possesses a central property of a global sensitivity measure and so it is considered hybrid local–global measure. obal Fourier amplitude sensitivity test (FAST) is added to the analysis and compared with both marginal and profile-based sensitivity methods. The Fourier sine amplitude is utilized here as a first-order sensitivity measure and shown to be directly linked to the local sensitivity coefficient averaged over all ranges of parameter uncertainties and so it is also considered hybrid local–global measure. The comparisons are explained by three compelling model cases with different degrees of parameter co-dependencies and nonlinearities.