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.
翻译:我们讨论了在系统生物学中经常应用的部分观测差异方程式的结构和实际可识别性问题。开发用于调查结构不可识别性的数学方法有着悠久的传统。最近还开发了检测和治疗结构不可识别性的高效计算方法。另一方面,实际不可识别性并没有在概念上同样清晰的层面上得到调查。我们认为,在模拟实验数据时,实际可识别性比结构可识别性更具挑战性。我们讨论了基于渔业信息矩阵的经典方法存在严重缺陷。我们建议使用剖析可能性,这是探测和解决实际不可识别性的有力方法。