Bayesian networks are one of the most widely used classes of probabilistic models for risk management and decision support because of their interpretability and flexibility in including heterogeneous pieces of information. In any applied modelling, it is critical to assess how robust the inferences on certain target variables are to changes in the model. In Bayesian networks, these analyses fall under the umbrella of sensitivity analysis, which is most commonly carried out by quantifying dissimilarities using Kullback-Leibler information measures. In this paper, we argue that robustness methods based instead on the familiar total variation distance provide simple and more valuable bounds on robustness to misspecification, which are both formally justifiable and transparent. We introduce a novel measure of dependence in conditional probability tables called the diameter to derive such bounds. This measure quantifies the strength of dependence between a variable and its parents. We demonstrate how such formal robustness considerations can be embedded in building a Bayesian network.

翻译：贝叶斯网络因其可解释性及整合异构信息源的灵活性，已成为风险管理和决策支持领域应用最广泛的概率模型之一。在任何应用建模中，评估特定目标变量的推断对模型变化的稳健性至关重要。在贝叶斯网络中，这类分析属于敏感性分析的范畴，通常通过基于Kullback-Leibler信息度量的差异量化方法实现。本文主张采用更为人熟知的总变差距离来构建稳健性分析方法，其能为模型设定偏误提供更简洁且更具实用价值的稳健性界，这些界限既具有形式上的可证明性，又具备直观透明性。为此，我们引入了一种称为"直径"的条件概率表依赖关系新度量来推导此类界限。该度量量化了变量与其父节点间依赖关系的强度。我们进一步展示了如何将此类形式化的稳健性考量嵌入贝叶斯网络的构建过程中。