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A Systematic Computational Framework for Practical Identifiability Analysis in Mathematical Models Arising from

Shun Wang1, Wenrui Hao1

  • 1Department of Mathematics, Penn State University, University Park, Pennsylvania, 16802, USA.

Advanced Science (Weinheim, Baden-Wurttemberg, Germany)
|July 22, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a new mathematical framework to assess parameter identifiability in biological models. It proves practical identifiability is linked to the Fisher Information Matrix, offering a faster, more reliable method for model analysis and experimental design.

Keywords:
optimal data collectionparameter regularizationpractical identifiabilityuncertainty quantification

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Area of Science:

  • Systems Biology
  • Mathematical Modeling
  • Computational Biology

Background:

  • Practical identifiability of parameters is crucial for reliable data-driven biological models.
  • Uncertainty in parameter estimation limits model predictions and decision-making.
  • Current methods for identifiability analysis can be computationally intensive.

Purpose of the Study:

  • To develop a novel mathematical framework for practical identifiability analysis in dynamic biological models.
  • To establish a rigorous definition and efficient assessment metric for parameter identifiability.
  • To provide methods for improving model reliability and guiding experimental design.

Main Methods:

  • Defined practical identifiability rigorously and proved its equivalence to Fisher Information Matrix (FIM) invertibility.
  • Established the relationship between practical and coordinate identifiability, introducing an efficient metric.
  • Incorporated regularization terms for non-identifiable parameters and developed an optimal experimental design algorithm.

Main Results:

  • Demonstrated that practical identifiability is equivalent to FIM invertibility.
  • Introduced an efficient metric for identifiability assessment, outperforming traditional profile likelihood methods.
  • Showcased the framework's effectiveness in improving uncertainty quantification and guiding experimental design through applications.

Conclusions:

  • The proposed framework offers a computationally efficient and rigorous approach to practical identifiability analysis.
  • This method enhances the reliability of biological models and aids in identifying key observable variables.
  • The framework facilitates informed experimental design for robust parameter estimation in biological systems.