We apply Likelihood-Ratio and $C(\alpha)$ tests to ODE models, and illustrate the null distributions and the powers of them. We found $C(\alpha)$ test is more resistant to errors of numerical solutions of OEDs.
We derive the explicit formulas of the two statistics in the ODE systems setting. We use c library Sundials.Cvodes to get the sensitivies of the ODEs and Levmar of a c implementation of the Levenberg--Marquardt algorithm for the optimization for the parameters. Finally we apply the two tests to predator-prey models.
|