Likelihood-Ratio and $C(\Alpha)$ Tests for ODE Models

• Activity Number: 518 - Software for Statistical Computing
• Type: Contributed
• Date/Time: Wednesday, August 2, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Yuping Yang* and Richard Lockhart and Jiguo Cao
• Companies: Simon Frase University and Simon Fraser University and Simon Frase University
• Keywords: Score test ; Likelihood-ratio ; sundials.cvodes

Abstract

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.