A Cautionary Tale of Model Misspecification and Identifiability

Area of Science:

• Mathematical Biology
• Computational Biology
• Systems Biology

Background:

• Mathematical models are crucial for interpreting biological data, aiding prediction and parameter estimation.
• Complex and non-identifiable models with limited data present significant challenges in mathematical biology.
• Model simplification for identifiability can paradoxically introduce misspecification and reduce accuracy.

Purpose of the Study:

• To demonstrate how structural uncertainty propagates to parameter estimates in mathematical biology.
• To explore the trade-offs between model identifiability, misspecification, and accuracy.
• To propose a method for delineating parameters of interest from model uncertainty.

Main Methods:

• Utilized a semi-parametric Gaussian process approach to quantify structural uncertainty.
• Applied the method to a generalized logistic growth model with an unknown crowding function.
• Investigated a spatially resolved partial differential equation model with time-dependent diffusivity.

Main Results:

• Allowing for structural model uncertainty resulted in more robust and accurate parameter estimates.
• The approach provided a better quantification of the remaining uncertainty in the model.
• Demonstrated that simplifying models can lead to catastrophic costs in accuracy.

Conclusions:

• Structural uncertainty is a critical factor in parameter estimation for complex biological models.
• Addressing model misspecification through uncertainty quantification enhances predictive power.
• The proposed Gaussian process method offers a robust alternative for analyzing biological systems with limited data.