Michael Hayes

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if the observed data do not show A and C to be independent, conditional on B, then we can safely conclude that the chain model is incompatible with the data and needs to be discarded (or repaired). Second, the graphical properties of the diagram dictate which causal models can be distinguished by data and which will forever remain indistinguishable, no matter how large the data. For example, we cannot distinguish the fork A ← B → C from the chain A → B → C by data alone because, with C listening to B only, the two imply the same independence conditions.
The Book of Why: The New Science of Cause and Effect (Penguin Science)
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