Robust Parameter Estimation in Dynamical Systems by Stochastic Differential Equations

TL;DR

This paper compares the robustness of parameter estimation in stochastic differential equations (SDEs) versus ordinary differential equations (ODEs), showing SDEs provide more stable estimates under various model misspecifications and data issues.

Contribution

It provides a comprehensive analysis of the robustness of SDEs in parameter estimation compared to ODEs, including simulations and real-world COVID-19 data.

Findings

SDEs offer more stable parameter estimates under noise and perturbations.

SDEs outperform ODEs in robustness when data is missing or models are simplified.

Simulation and COVID-19 data analysis confirm the advantages of SDEs.

Abstract

Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing robustness to noise and model misspecifications. Recent research highlights the statistical advantages of SDEs, such as improved parameter identifiability and stability under perturbations. This paper investigates the robustness of parameter estimation in SDEs versus ODEs under three types of model misspecifications: unrecognized noise sources, external perturbations, and simplified models. Furthermore, the effect of missing data is explored. Through simulations and an analysis of Danish COVID-19 data, we demonstrate that SDEs yield more stable and reliable parameter estimates, making them a strong alternative to traditional ODE modeling in the presence of uncertainty.