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A Cautionary Tale of Model Misspecification and Identifiability.

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Simplifying complex biological models can lead to inaccurate parameter estimates. Accounting for structural uncertainty improves model accuracy and quantifies remaining uncertainty in mathematical biology.

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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.