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Making Predictions Using Poorly Identified Mathematical Models.

Matthew J Simpson1, Oliver J Maclaren2

  • 1School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia. matthew.simpson@qut.edu.au.

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Summary
This summary is machine-generated.

This study introduces Profile-Wise Analysis (PWA) for mathematical biology models with parameter non-identifiability. PWA offers a unified, interpretable framework for estimation and prediction, even with partially identifiable parameters.

Keywords:
Model predictionParameter estimationParameter identifiabilityProfile likelihood

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Area of Science:

  • Mathematical Biology
  • Computational Biology
  • Systems Biology

Background:

  • Mathematical models in biology frequently suffer from parameter non-identifiability, impacting model reliability.
  • Practical non-identifiability arises from data limitations, hindering precise parameter estimation.
  • Existing methods often struggle with models where only some parameters are identifiable.

Purpose of the Study:

  • To apply the Profile-Wise Analysis (PWA) workflow to non-identifiable mathematical biology models for the first time.
  • To demonstrate PWA's utility in a unified framework for identifiability, parameter estimation, and prediction.
  • To illustrate PWA's application to both structurally and practically non-identifiable models using simple population growth examples.

Main Methods:

  • Utilized the Profile-Wise Analysis (PWA), a recent likelihood-based workflow.
  • Applied PWA to simple population growth models exhibiting structural and practical non-identifiability.
  • Compared PWA prediction intervals with gold-standard full likelihood prediction intervals using provided Julia code.

Main Results:

  • Successfully applied PWA to non-identifiable models, demonstrating its capability beyond idealized problems.
  • Showcased PWA as a systematic approach to handling parameter non-identifiability in mathematical models.
  • Illustrated how PWA provides insightful and interpretable analysis of parameter uncertainty's impact on model predictions.

Conclusions:

  • Profile-Wise Analysis (PWA) provides a systematic and interpretable method for addressing parameter non-identifiability in mathematical biology.
  • PWA effectively handles models with both structural and practical non-identifiability, including scenarios with partially identifiable parameters.
  • The workflow offers valuable insights into how parameter uncertainty influences model predictions, enhancing model understanding and reliability.