An easy and efficient approach for testing identifiability of parameters

Abstract: The feasibility of uniquely estimating parameters of dynamical systems from observations is a widely discussed aspect of mathematical modelling. Several approaches have been published for analyzing identifiability. However, they are typically computationally demanding, difficult to perform and/or not applicable in many application settings. Here, an intuitive approach is presented which enables quickly testing of parameter identifiability. Numerical optimization with a penalty in radial direction enforcing displacement of the parameters is used to check whether estimated parameters are unique, or whether the parameters can be altered without loss of agreement with the data indicating non-identifiability. This Identifiability-Test by Radial Penalization (ITRP) can be employed for every model where optimization-based fitting like least-squares or maximum likelihood is feasible and is therefore applicable for all typical deterministic models. The approach is illustrated and tested using 11 ordinary differential equation (ODE) models. The presented approach can be implemented without great efforts in any modelling framework. It is available within the free Matlab-based modelling toolbox Data2Dynamics. Source code is available at https://github.com/Data2Dynamics.