Determining structural parameter identifiability in biological dynamical models by analysing the statistical properties of the likelihood behaviour

Identifiability is a fundamental precondition for model identification and concerns the possibility to determine unique parameters sets using a certain model structure and the experimental observations for the model input-output. In this article we show how to a priori assess the identifiability of model parameters analysing the properties of the likelihood function. More precisely, a model is identifiable if the likelihood function shows a unique absolute minimum beyond the confidence intervals. The study of the likelihood function cannot avoid accompanying the likelihood estimates with the assessment of the confidence intervals, which reflect the variability in experimental data. We then show the results of this approach in cases of biotechnological relevance where the identifiability has been previously assessed.