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

by Judea Pearl

A to C means that if we could wiggle only A, then we would expect to see a change in the probability of C. A missing arrow from A to C means that in the same experiment we would not see any change in C, once we held constant the parents of C (in other words, B in the example above). Note that the probabilistic expression “once we know the value of B” has given way to the causal expression “once we hold B constant,” which implies that we are physically preventing B from varying and disabling the arrow from A to B. The causal thinking that goes into the construction of the causal network will pay off, of course, in the type of questions the network can answer. Whereas a Bayesian network can only tell us how likely one event is, given that we observed another (rung-one information), causal diagrams can answer interventional and counterfactual questions. For example, the causal fork A B C tells us in no uncertain terms that wiggling A would have no effect on C, no matter how intense the wiggle. On the other hand, a Bayesian network is not equipped to handle a “wiggle,” or to tell the difference between seeing and doing, or indeed to distinguish a fork from a chain.