Structural Estimation of Partially Observed Linear Non-Gaussian Acyclic Model: A Practical Approach with Identifiability

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. Highlights • With recent advances, identifying structural identifiability is no longer a major issue • Practical identifiability is still challenging • Fisher information matrix is misleading • Profile likelihood can solve practical identifiability challenge