As we discussed in Section 4.2, the graph for the interventional distribution 𝑃(𝑌 | do(𝑡)) is the same as the graph for the observational distribution 𝑃(𝑌, 𝑇, 𝑋) , but with the incoming edges to 𝑇 removed. For example, if we take the graph from Figure 4.5 and intervene on 𝑇 , then we get the manipulated graph in Figure 4.6. In this manipulated graph, there cannot be any backdoor paths because no edges are going into the backdoor of 𝑇 . Therefore, all of the association that flows from 𝑇 to 𝑌 in the manipulated graph is purely causal.
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- (no access) - Introduction_to_Causal_Inference-Nov19_2020-Neal.pdf, p45
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