Critical Assessment of Parameter Estimation Methods in Models of Biological Oscillators ⁎ ⁎ This project has received funding from the European Unions Horizon 2020 research and innovation program under grant agreement 675585 (Marie Sklodowska-Curie ITN SyMBioSys). The authors JAP and LG are Marie Sklodowska-Curie Early Stage Researchers at IIM-CSIC (Spain) and PSE Ltd (UK) respectively.

Many biological systems exhibit oscillations in relation to key physiological or cellular functions, such as circadian rhythms, mitosis and DNA synthesis. Mathematical modelling provides a powerful approach to analysing these biosystems. Applying parameter estimation methods to calibrate these models can prove a very challenging task in practice, due to the presence of local solutions, lack of identifiability, and risk of overfitting. This paper presents a comparison of three state-of-the-art methods: frequentist, Bayesian and set-membership estimation. We use the Fitzhugh-Nagumo model with synthetic data as a case study. The computational performance and robustness of these methods is discussed, with a particular focus on their predictive capability using cross-validation.