Employing observability rank conditions for taking into account experimental information a priori

by Alejandro F. Villaverde

A dynamic model is identifiable if it is possible to infer its parameters by measuring its output over time. Likewise, it is observable if it is possible to determine its state variables in the same way. Since parameters can be treated as constant state variables, identifiability can be considered as a particular case of observability. Thus, both properties can be analysed by building an observability matrix and checking whether it has full rank. This test can be performed before collecting experimental data (i.e., “a priori”), and it may reveal structural issues of the model equations. Here we explore whether such a test can be extended to assess the influence of experimental characteristics, including the number of experiments.

Left: noiseless simulation of the model output (black line) and artificial noisy data (red circles) used for parameter estimation. Right: bootstrap results for the estimation of one of the model parameters. It can be seen that the parameter can be estimated accurately, despite the difficulty of determining high order derivatives of the output measurements.