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.

翻译：提出了一种基于信息论估计量的方法，用于在实践考量下评估统计模型的全局可辨识性。该框架建立在贝叶斯统计框架内，为在偶然不确定性和认知不确定性下进行参数估计奠定了基础。在构建该估计量时，未对统计模型的结构或先验分布做出任何假设。该估计量具有以下显著优势：首先，进行实践可辨识性分析无需受控实验或数据；其次，可考虑模型形式、参数或测量等不同形式的不确定性；第三，该可辨识性分析是全局性的，而非依赖于参数的具体实现。若单个参数可辨识性较低，其可能归属于某个可辨识子集，使得该子集内参数间存在函数关系，从而对统计模型产生联合影响。本文扩展了实践可辨识性框架，通过突出后验涌现的参数对依赖关系来发现可辨识参数子集。考察单个参数的实践可辨识性及其与其他参数的依赖关系，对以估计为中心的参数化及模型选择具有重要参考价值。通过线性高斯模型和非线性甲烷-空气简化动力学模型验证了该方法的适用性。