Model Identifiability

Once we have built a model to describe the dynamics of a network, in order to simulate this dynamic, that is, the evolution of the network over time, we need to know the parameters of the model. Very often the values of the kinetic constants in a network of biochemical interactions, or more generally the arc weights on the network defining the force and direction of the interaction between nodes, are obtained from experimental data through various regression and inference techniques. In this chapter, we will tackle a problem that is upstream of the parameter estimation, that is, the possibility to infer them from the data. This is the problem of identifiability. Identifiability is a fundamental prerequisite for model identification. It concerns uniqueness of the model parameters determined from experimental observations. This chapter specifically deals with structural or a priori identifiability: whether or not parameters can be identified from a given model structure and experimental measurements. Since experimental data are usually affected by uncertainties this question is known as practical identifiability. Non-identifiability of parameters induces non-observability of trajectories, reducing the predictive power of the model. We discuss here a method of parameter identifiability based on the observability rank test and we discuss its suitability for handling noisy observations.