Data-informed model reduction for inference and prediction from non-identifiable models.

Area of Science:

• Theoretical Biology
• Computational Biology
• Mathematical Modeling

Background:

• Parameter identifiability is a common challenge in theoretical biology mathematical models.
• Non-identifiability hinders the mechanistic interpretation of observations from these models.
• Existing methods like reparameterization often neglect the impact of noisy, finite data.

Purpose of the Study:

• To present a computational approach for model reduction via likelihood reparameterization.
• To address both structural and practical non-identifiability issues in mathematical models.
• To enable computationally efficient, model-based predictions from reduced, identifiable models.

Main Methods:

• Developed a simple computational approach for likelihood reparameterization.
• Applied the method to reduce non-identifiable continuum models based on differential equations.
• Incorporated various noise models to link model solutions with noisy observations.

Main Results:

• Successfully constructed simplified, identifiable mathematical models.
• Demonstrated the application of the method to diverse differential equation classes.
• Illustrated efficient model-based predictions from reduced models using computational experiments.

Conclusions:

• The proposed likelihood reparameterization offers an effective strategy for addressing non-identifiability in mathematical models.
• This approach facilitates robust model-based predictions even with noisy, limited data.
• The method enhances the utility of mathematical models in theoretical biology for mechanistic understanding and prediction.