  We may attempt to encapsulate what we know about a physical system by a model
structure, $S$. This collection of related models is defined by parametric
relationships between system features; say observables (outputs), unobservable
variables (states), and applied inputs. Each parameter vector in some parameter
space is associated with a completely specified model in $S$. Before choosing a
model in $S$ to predict system behaviour, we must estimate its parameters from
system observations. Inconveniently, multiple models (associated with distinct
parameter estimates) may approximate data equally well. Yet, if these equally
valid alternatives produce dissimilar predictions of unobserved quantities,
then we cannot confidently make predictions. Thus, our study may not yield any
useful result. We may anticipate the non-uniqueness of parameter estimates
ahead of data collection by testing $S$ for structural global identifiability
(SGI). Here we will provide an overview of the importance of SGI, some
essential theory and distinctions, and demonstrate these in testing some
examples.
