In this contribution, we present and analyze datasnooping in the context of the DIA method. As the DIA method for the detection, identification and adaptation of mismodelling errors is concerned with estimation and testing, it is the combination of both that needs to be considered. This combination is rigorously captured by the DIA estimator. We discuss and analyze the DIA-datasnooping decision probabilities and the construction of the corresponding partitioning of misclosure space. We also investigate the circumstances under which two or more hypotheses are nonseparable in the identification step. By means of a theorem on the equivalence between the nonseparability of hypotheses and the inestimability of parameters, we demonstrate that one can forget about adapting the parameter vector for hypotheses that are nonseparable. However, as this concerns the complete vector and not necessarily functions of it, we also show that parameter functions may exist for which adaptation is still possible. It is shown how this adaptation looks like and how it changes the structure of the DIA estimator. To demonstrate the performance of the various elements of DIA-datasnooping, we apply the theory to some selected examples. We analyze how geometry changes in the measurement setup affect the testing procedure, by studying their partitioning of misclosure space, the decision probabilities and the minimal detectable and identifiable biases. The difference between these two minimal biases is highlighted by showing the difference between their corresponding contributing factors. We also show that if two alternative hypotheses, say $${\mathcal {H}}_{i}$$Hi and $${\mathcal {H}}_{j}$$Hj, are nonseparable, the testing procedure may have different levels of sensitivity to $${\mathcal {H}}_{i}$$Hi-biases compared to the same $${\mathcal {H}}_{j}$$Hj-biases.

中文翻译：

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DIA-数据监听和可识别性

在这篇文章中，我们在 DIA 方法的背景下展示和分析了数据监听。由于用于检测、识别和适应误建模错误的 DIA 方法涉及估计和测试，因此需要考虑两者的结合。这种组合由 DIA 估计器严格捕获。我们讨论和分析了 DIA-datasnooping 决策概率和相应的不闭合空间分区的构建。我们还调查了在识别步骤中两个或多个假设不可分离的情况。通过假设不可分离性和参数不可估计性之间等价的定理，我们证明人们可以忘记为不可分离的假设调整参数向量。然而，由于这涉及完整的向量而不一定是它的函数，因此我们还表明可能存在参数函数，但仍然可以进行适应。它显示了这种适应的样子以及它如何改变 DIA 估计器的结构。为了演示 DIA-datasnooping 的各种元素的性能，我们将理论应用于一些选定的示例。我们分析了测量设置中的几何变化如何影响测试过程，通过研究它们对不闭合空间的划分、决策概率以及最小的可检测和可识别偏差。这两个最小偏差之间的差异通过显示它们相应的影响因素之间的差异来突出显示。我们还表明，如果有两个替代假设，比如 $${\mathcal {H}}_{i}$$Hi 和 $${\mathcal {H}}_{j}$$Hj，