Sensitivity analysis and identifiability for differential equation models

Sensitivity analysis in the statistical identification of dynamic models uses the first partial derivatives of the process variables with respect to the parameters. Sensitivities have two main uses, as gradients in Newton type optimizers for least squares fitting, and as a component in the computation of the Fisher information matrix used for asymptotic testing and confidence regions. We give a brief review of one reliable method for calculating sensitivities. Then two types of identifiability based on the sensitivities are discussed. The first corresponds to non-singularity of the information matrix mentioned above, obtained by using observations at separate time points. The second, which draws on the Taylor series method and differential algebra methods, corresponds to local identifiability. This is when the process and as many of its time derivatives as necessary are observed. These two types of identifiability are shown to be equivalent.