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.
翻译:我们可能试图用模型结构($S$)来概括我们所了解的物理系统的情况。这种相关模型的收集是通过系统特征之间的参数关系来界定的;说可观测值(产出)、不可观测变量(状态)和应用投入。某些参数空间的每个参数矢量都与一个完全指定的模型($S美元)有关。在选择一个以美元计算的模型来预测系统行为之前,我们必须从系统观测中估计其参数。自然地,多种模型(与不同的参数估计有关)可能同样接近数据。然而,如果这些同样有效的替代方法对未观测的数量作出不同预测,那么我们就无法有信心地作出预测。因此,我们的研究可能不会产生任何有用的结果。我们可以预测,在数据收集之前,通过测试美元作为结构性全球可识别性(SGI)的模型,我们在这里将概述SGI的重要性、一些基本理论和区别,并在测试一些例子时展示这些参数。