Usefulness of structural identifiability when practical identifiability is absent

Ascertain whether ideal structural identifiability results—defined as injectivity of the parameter-to-data-distribution mapping under perfect data—are useful for inference and model development in scenarios where, at the observation grid level with finite noisy data, the parameters are practically non-identifiable.

Background

The paper distinguishes structural identifiability (uniqueness under perfect data) from practical identifiability (estimability with finite, noisy observations) and introduces an auxiliary mapping from parameters to data-distribution parameters. It notes that matching structural identifiability requires working at the solution grid level, while practical analyses operate at the observation grid level.

In ill-posed problems or models with parameter-dependent limiting behavior, the auxiliary mapping can exhibit arbitrarily small singular values in certain regions, blurring the distinction between practical and structural non-identifiability. This context raises a foundational question about the practical value of structural identifiability conclusions in settings where practical identifiability fails.

References

Furthermore, it is unclear if ideal structural identifiability results are useful in the absence of practical identifiability.

— Invariant Image Reparameterisation: A Unified Approach to Structural and Practical Identifiability and Model Reduction  (2502.04867 - Maclaren et al., 7 Feb 2025) in Methods, Subsection 'Practical vs structural identifiability and observation operators'

It is unclear whether this parameter is identifiable or not, given the bias away from the true parameter values are around 5%.

— Parameter identifiability of a neuroendocrine-inflammatory model across experimental designs  (2609.30031 - Ayres et al., 24 Sep 2026) in Section 4.2, subsection “Global Optimization”