Notes on Forré's Notion of Conditional Independence and Causal Calculus for Continuous Variables

• URL: http://arxiv.org/abs/2603.24333v1
• Date: Wed, 25 Mar 2026 14:13:23 GMT
• Title: Notes on Forré's Notion of Conditional Independence and Causal Calculus for Continuous Variables
• Abstract summary: Original paper establishes a strong global Markov property connecting transitional conditional independencies.<n>These notes aim to further illustrate the motivations behind this framework and its connections to the literature.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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