The Book of Why: The New Science of Cause and Effect

by Judea Pearl

This has two enormously important implications. First, it tells us that causal assumptions cannot be invented at our whim; they are subject to the scrutiny of data and can be falsified. For instance, 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 the two diagrams imply the same independence conditions. Another convenient way of thinking about the causal model is in terms of hypothetical experiments. Each arrow can be thought of as a statement about the outcome of a hypothetical experiment.