Robust Estimation for Ordinary Differential Equation Models
Article first published online: 14 MAR 2011
© 2011, The International Biometric Society
Volume 67, Issue 4, pages 1305–1313, December 2011
How to Cite
Cao, J., Wang, L. and Xu, J. (2011), Robust Estimation for Ordinary Differential Equation Models. Biometrics, 67: 1305–1313. doi: 10.1111/j.1541-0420.2011.01577.x
- Issue published online: 14 DEC 2011
- Article first published online: 14 MAR 2011
- Received April 2010. Revised November 2010. Accepted December 2010.
- Dynamic model;
- Predator–prey system;
- Robust penalized smoothing;
- System identification
Summary Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic processes that arise in biology, engineering, medicine, and many other areas. It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. We propose a robust method to address this problem. The dynamic process is represented with a nonparametric function, which is a linear combination of basis functions. The nonparametric function is estimated by a robust penalized smoothing method. The penalty term is defined with the parametric ODE model, which controls the roughness of the nonparametric function and maintains the fidelity of the nonparametric function to the ODE model. The basis coefficients and ODE parameters are estimated in two nested levels of optimization. The coefficient estimates are treated as an implicit function of ODE parameters, which enables one to derive the analytic gradients for optimization using the implicit function theorem. Simulation studies show that the robust method gives satisfactory estimates for the ODE parameters from noisy data with outliers. The robust method is demonstrated by estimating a predator–prey ODE model from real ecological data.