d-separation Implies Association is Causation

Given that we have tools to measure association, how can we isolate causation? In other words, how can we ensure that the association we measure is causation, say, for measuring the causal effect of 𝑋 on 𝑌 ? Well, we can do that by ensuring that there is no non-causal association flowing between 𝑋 and 𝑌 . This is true if 𝑋 and 𝑌 are d-separated in the augmented graph where we remove outgoing edges from 𝑋 . This is because all of 𝑋 ’s causal effect on 𝑌 would flow through it’s outgoing edges, so once those are removed, the only association that remains is purely non-causal association