Structural parameter identifiability is a property of a differential model with parameters that
allows for the parameters to be determined from the model equations in the absence of
noise. One of the standard approaches to assessing this problem is via input–output
equations and, in particular, characteristic sets of differential ideals. The precise relation
between identifiability and input–output identifiability is subtle. The goal of this note is to
clarify this relation. The main results are: identifiability implies input–output identifiability; …