The Book of Why: The New Science of Cause and Effect (Penguin Science)

by Judea Pearl

Suppose you’ve just landed in Zanzibar after making a tight connection in Aachen, and you’re waiting for your suitcase to appear on the carousel. Other passengers have started to get their bags, but you keep waiting … and waiting … and waiting. What are the chances that your suitcase did not actually make the connection from Aachen to Zanzibar? The answer depends, of course, on how long you have been waiting. If the bags have just started to show up on the carousel, perhaps you should be patient and wait a little bit longer. If you’ve been waiting a long time, then things are looking bad. We can quantify these anxieties by setting up a causal diagram (Figure 3.5). FIGURE 3.5. Causal diagram for airport/bag example. This diagram reflects the intuitive idea that there are two causes for the appearance of any bag on the carousel. First, it had to be on the plane to begin with; otherwise, it will certainly never appear on the carousel. Second, the presence of the bag on the carousel becomes more likely as time passes … provided it was actually on the plane. To turn the causal diagram into a Bayesian network, we have to specify the conditional probability tables. Let’s say that all the bags at Zanzibar airport get unloaded within ten minutes. (They are very efficient in Zanzibar!) Let’s also suppose that the probability your bag made the connection, P(bag on plane = true) is 50 percent. (I apologize if this offends anybody who works at the Aachen airport. I am only following Co...