A Consistent Direct Method for Estimating Parameters in Ordinary Differential Equations Models

Abstract

Ordinary differential equations provide an attractive framework for modeling temporal dynamics in a variety of scientific settings. We show how consistent estimation for parameters in ODE models can be obtained by modifying a direct (non-iterative) least squares method similar to the direct methods originally developed by Himmelbau, Jones and Bischoff. Our method is called the bias-corrected least squares (BCLS) method since it is a modification of least squares methods known to be biased. Consistency of the BCLS method is established and simulations are used to compare the BCLS method to other methods for parameter estimation in ODE models.