Recently, Forré (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes a strong global Markov property connecting transitional conditional independencies with suitable graphical separation criteria for directed mixed graphs with input nodes (iDMGs), together with a version of causal calculus for iDMGs in a general measure-theoretic setting. These notes aim to further illustrate the motivations behind this framework and its connections to the literature, highlight certain subtlies in the general measure-theoretic causal calculus, and extend the "one-line" formulation of the ID algorithm of Richardson et al. (Ann. Statist. 51(1):334--361, 2023) to the general measure-theoretic setting.

翻译：近日，Forré（arXiv:2104.11547, 2021）引入了过渡条件独立性这一概念，它为随机变量与非随机变量提供了统一的条件独立性框架。原文建立了强全局马尔可夫性质，将过渡条件独立性与含输入节点的有向混合图（iDMGs）的恰当图分离准则相联系，并在一般测度论框架下提出了适用于iDMGs的因果演算版本。本笔记旨在进一步阐明该框架背后的动机及其与现有文献的联系，突出一般测度论因果演算中的某些微妙之处，并将Richardson等人（Ann. Statist. 51(1):334–361, 2023）提出的ID算法“单行”表达式推广至一般测度论框架。