A novel information-theoretic approach is proposed to assess the global practical identifiability of Bayesian statistical models. Based on the concept of conditional mutual information, an estimate of information gained for each model parameter is used to quantify the identifiability with practical considerations. 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, unlike popular variance-based global sensitivity analysis methods, different forms of uncertainties, such as model-form, parameter, or measurement can be taken into account; third, the identifiability analysis is global, and therefore independent of a realization of the 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. The applicability of the proposed approach is demonstrated using a linear Gaussian model and a non-linear methane-air reduced kinetics model. It is shown that by examining the information gained for each model parameter along with its dependencies with other parameters, a subset of parameters that can be estimated with high posterior certainty can be found.

翻译：提出一种新颖的信息论方法，用于评估贝叶斯统计模型全局可辨识性的实际能力。基于条件互信息概念，通过估计每个模型参数的信息增益，结合实际问题考量对可辨识性进行量化。在构建估计量时，不对统计模型结构或先验分布作任何假设。该估计量具有以下显著优势：首先，无需进行受控实验或获取特定数据即可进行实际可辨识性分析；其次，相较于流行的基于方差的全局敏感性分析方法，可纳入模型形式、参数或测量等不同类型的不确定性；第三，可辨识性分析具有全局性，因此不依赖于参数的具体实现值。若某参数可辨识性较低，它可能属于可辨识参数子集——该子集内参数存在函数关系，从而对统计模型产生联合影响。我们扩展了实际可辨识性框架，通过突出显示后验涌现的参数对依赖关系，寻找可辨识参数子集。利用线性高斯模型和非线性甲烷-空气简化动力学模型验证了所提方法的适用性。结果表明，通过考察各模型参数的信息增益及其与其他参数的依赖关系，可找到具有高后验确定性的可估参数子集。