On structural and practical identifiability

TL;DR

This paper examines the differences between structural and practical identifiability in differential equation models, highlighting the limitations of traditional methods and proposing profile likelihood as a more effective approach for practical identifiability issues.

Contribution

It introduces the use of profile likelihood as a robust method to detect and address practical non-identifiability in systems biology models.

Findings

Profile likelihood effectively detects practical non-identifiability.

Classical Fisher information matrix approach has significant shortcomings.

Practical identifiability is more challenging than structural identifiability.

Abstract

We discuss issues of structural and practical identifiability of partially observed differential equations which are often applied in systems biology. The development of mathematical methods to investigate structural non-identifiability has a long tradition. Computationally efficient methods to detect and cure it have been developed recently. Practical non-identifiability on the other hand has not been investigated at the same conceptually clear level. We argue that practical identifiability is more challenging than structural identifiability when it comes to modelling experimental data. We discuss that the classical approach based on the Fisher information matrix has severe shortcomings. As an alternative, we propose using the profile likelihood, which is a powerful approach to detect and resolve practical non-identifiability.