Model Selection for Ordinary Differential Equations: A Statistical Testing Approach

Area of Science:

• Mathematical modeling
• Computational science
• Statistical analysis

Background:

• Ordinary differential equations (ODEs) are crucial for modeling complex dynamics in science.
• Selecting the appropriate ODE model from multiple options, especially with statistical noise, poses a significant challenge.
• Existing methods often require models to be nested, limiting the comparison of diverse explanations.

Purpose of the Study:

• To develop a robust, testing-based approach for selecting among ordinary differential equation (ODE) models.
• To enable the comparison and ranking of non-nested ODE models, accommodating different mechanistic understandings.
• To provide a practical tool for ODE model selection in the presence of statistical noise.

Main Methods:

• Adaptation of classical statistical paradigms (Vuong and Hotelling tests) for ODE model misspecification.
• Development of a testing framework to compare and rank diverse ODE models.
• Numerical simulations to evaluate the statistical properties (size and power) of the proposed test.
• Application of the method to real-world datasets.

Main Results:

• The proposed testing approach effectively selects ODE models even with statistical noise.
• Simulation studies confirmed the test achieves nominal size and power across various scenarios.
• Real-world data examples demonstrated the practical utility and applicability of the algorithm.

Conclusions:

• The developed method offers a flexible and powerful solution for ODE model selection.
• The approach facilitates the comparison of non-nested models, advancing causal explanation in scientific modeling.
• A Python implementation is provided to promote accessibility and adoption by the scientific community.