On structural and practical 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 nonidentifiability has a long tradition. Computationally efficient methods to detect and cure it have been developed recently. Practical nonidentifiability, 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 modeling 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 nonidentifiability.