Global Identifiability Analysis of Statistical Models using an Information-Theoretic Estimator in a Bayesian Framework

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.