Model Selection for Ordinary Differential Equations: a Statistical Testing Approach

TL;DR

This paper proposes a statistical testing approach for selecting among multiple ODE models representing the same phenomenon, addressing model uncertainty with a robust, non-nested comparison method validated through simulations and real data.

Contribution

It adapts classical statistical tests to the ODE context for model selection, providing a novel, non-nested comparison framework validated by simulations and real data applications.

Findings

The proposed test is consistent in size and power.

Simulation studies confirm theoretical robustness.

Real-world examples demonstrate practical applicability.

Abstract

Ordinary differential equations (ODEs) are foundational in modeling intricate dynamics across a gamut of scientific disciplines. Yet, a possibility to represent a single phenomenon through multiple ODE models, driven by different understandings of nuances in internal mechanisms or abstraction levels, presents a model selection challenge. This study introduces a testing-based approach for ODE model selection amidst statistical noise. Rooted in the model misspecification framework, we adapt foundational insights from classical statistical paradigms (Vuong and Hotelling) to the ODE context, allowing for the comparison and ranking of diverse causal explanations without the constraints of nested models. Our simulation studies validate the theoretical robustness of our proposed test, revealing its consistent size and power. Real-world data examples further underscore the algorithm's applicability in practice. To foster accessibility and encourage real-world applications, we provide a user-friendly Python implementation of our model selection algorithm, bridging theoretical advancements with hands-on tools for the scientific community.