An information-theoretic estimator is proposed to assess the global
identifiability of statistical models with practical consideration. The
framework is formulated in a Bayesian statistical setting which is the
foundation for parameter estimation under aleatoric and epistemic uncertainty.
No assumptions are made about the structure of the statistical model or the
prior distribution while constructing the estimator. The estimator has the
following notable advantages: first, no controlled experiment or data is
required to conduct the practical identifiability analysis; second, different
forms of uncertainties, such as model form, parameter, or measurement can be
taken into account; third, the identifiability analysis is global, rather than
being dependent on a realization of parameters. If an individual parameter has
low identifiability, it can belong to an identifiable subset such that
parameters within the subset have a functional relationship and thus have a
combined effect on the statistical model. The practical identifiability
framework is extended to highlight the dependencies between parameter pairs
that emerge a posteriori to find identifiable parameter subsets. Examining the
practical identifiability of an individual parameter along with its
dependencies with other parameters is informative for an estimation-centric
parameterization and model selection. The applicability of the proposed
approach is demonstrated using a linear Gaussian model and a non-linear
methane-air reduced kinetics model