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

TL;DR

This paper introduces a bias-corrected least squares (BCLS) method for consistent parameter estimation in ordinary differential equation models, improving upon traditional biased direct methods.

Contribution

The paper develops and proves the consistency of the BCLS method, a novel modification of direct least squares techniques for ODE parameter estimation.

Findings

BCLS method is consistent for parameter estimation.

Simulation results show BCLS outperforms existing methods.

BCLS reduces bias in direct estimation approaches.

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.