Identification of dynamical biological systems based on random effects models

System identification is a data-driven modeling approach more and more used in biology and biomedicine. In this application context, each assay is always repeated to estimate the response variability. The inference of the modeling conclusions to the whole population requires to account for the inter-individual variability within the modeling procedure. One solution consists in using random effects models but up to now no similar approach exists in the field of dynamical system identification. In this article, we propose a new solution based on an ARX (Auto Regressive model with eXternal inputs) structure using the EM (Expectation-Maximisation) algorithm for the estimation of the model parameters. Simulations show the relevance of this solution compared with a classical procedure of system identification repeated for each subject.