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Experimental Methods to Study Human Postural Control
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Published on: September 11, 2019

Parameter identifiability and redundancy: theoretical considerations.

Mark P Little1, Wolfgang F Heidenreich, Guangquan Li

  • 1Department of Epidemiology and Public Health, Imperial College Faculty of Medicine, London, United Kingdom. mark.little@imperial.ac.uk

Plos One
|January 30, 2010
PubMed
Summary
This summary is machine-generated.

Identifying unidentifiable or redundant parameters in complex biological models is crucial for accurate data analysis. This study shows that concepts like weak local identifiability largely coincide with traditional parameter identifiability within the exponential family.

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Area of Science:

  • Mathematical Biology
  • Systems Biology
  • Computational Biology

Background:

  • Complex biological models often contain numerous parameters.
  • Some parameters may be unidentifiable through regression analysis, leading to ill-defined models.
  • Parameter redundancy, where parameters can be expressed in terms of others, is closely related to identifiability.

Purpose of the Study:

  • To outline general considerations for parameter identifiability in complex biological systems.
  • To introduce and define weak local identifiability and gradient weak local identifiability.
  • To relate these new concepts to existing notions of parameter identifiability and redundancy.

Main Methods:

  • Analysis of local properties of the likelihood function, specifically the rank of the Hessian matrix.
  • Comparison of weak local identifiability and gradient weak local identifiability with established identifiability and redundancy concepts.
  • Application of these concepts to generalized cancer models.

Main Results:

  • Weak local identifiability and gradient weak local identifiability are introduced and defined.
  • Within the exponential family, parameter irredundancy, local identifiability, gradient weak local identifiability, and weak local identifiability are shown to be largely equivalent.
  • The concepts are applied to recently developed cancer models.

Conclusions:

  • Parameter local identifiability and redundancy are closely linked to weak local identifiability and gradient weak local identifiability.
  • Within the exponential family, these identifiability concepts largely coincide, simplifying model analysis.
  • This work provides a framework for assessing parameter identifiability in complex biological models, including cancer models.