Guaranteed numerical alternatives to structural identifiability testing

Testing models for structural identifiability is particularly important for knowledge-based models. If several values of the parameter vector lead to the same observed behavior of the model, then one may try to modify the experimental setup to eliminate this ambiguity (qualitative experiment design). The tediousness of the algebraic manipulations involved makes computer algebra particularly attractive. The purpose of the paper is to explore an alternative route based on guaranteed numerical computation. A new definition of identifiability in a domain allows testing to be cast into the framework of constraint-satisfaction problems, and makes it possible to use the tools of interval analysis and interval constraint propagation to get guaranteed answers. When the data have already been collected, the notion of structural identifiability may not be the most pertinent concept. The paper shows how interval analysis and interval constraint propagation can again be used to bypass the identifiability study and estimate even parameters that are not identifiable uniquely