In causal inference and Bayesian graphical models, the idea of "marginalization" and being "closed under marginalization and conditioning" is brought up and referred to in "Ancestral Markov Graphs" paper (https://projecteuclid.org/journals/annals-of-statistics/volume-30/issue-4/Ancestral-graph-Markov-models/10.1214/aos/1031689015.full).
My question is:
- how does this relate to marginalization and conditioning in probability distributions?
- What does it mean intuitively for a graphical model to be "closed under marginalization and conditioning"?
- What is an example of a graphical model that is not?
A related discussion on marginalization in probability distributions: What does it mean to "marginalise out" something?