Guaranteed Numerical Computation as an Alternative to Computer Algebra for Testing Models for Identifiability

Testing parametric models for identifiability is particularly important for knowledge-based models. If several values of the parameter vector lead to the same observed behavior, then one may try to modify the experimental set-up to eliminate this ambiguity (which corresponds to performing qualitative experiment design). The tediousness of the algebraic operations involved in such tests makes computer algebra particularly attractive. This paper describes some limitations of this classical approach and explores an alternative route based on new definitions of identifiability and numerical tests implemented in a guaranteed way. The new approach is illustrated in the context of compartmental modeling, widely used in biology.