In this short note, I derive the Bell-CHSH inequalities as an elementary result in the present-day theory of statistical causality based on graphical models or Bayes' nets, defined in terms of DAGs (Directed Acyclic Graphs) representing direct statistical causal influences between a number of observed and unobserved random variables. I show how spatio-temporal constraints in loophole-free Bell experiments, and natural classical statistical causality considerations, lead to Bell's notion of local hidden variables, and thence to the CHSH inequalities. The word "local" applies to the way that the chosen settings influence the observed outcomes. The case of contextual setting-dependent hidden variables (thought of as being located in the measurement devices and dependent on the measurement settings) is automatically covered, despite recent claims that Bell's conclusions can be circumvented in this way.

翻译：在这篇简短的笔记中，我推导出贝尔-CHSH不等式作为当代基于图形模型或贝叶斯网络的统计因果理论的基本结果，这些模型以有向无环图（DAGs）定义，表示多个观测和未观测随机变量之间的直接统计因果影响。我展示了无漏洞贝尔实验中的时空约束以及自然经典统计因果考虑如何导致贝尔的局部隐变量概念，进而得出CHSH不等式。“局部”一词适用于所选设置影响观测结果的方式。尽管最近有声称可以通过上下文依赖的设置相关隐变量（被认为位于测量设备中且依赖于测量设置）来规避贝尔结论，但这种情况已被自动涵盖。