the book of why

Causal Diagram and Bayesian Network (Part 2)

There are three building blocks of Baysian Network. Remember that a Bayesian Network is nothing but some arrows connecting with different nodes representing the conditional probability table. The so-called building blocks are just the three types of arrow patterns.

Arrow Pattern	Easy To RMB Name	Description
A –> B –> C	Chain	Fire -> Smoke –> Alarm Conditioned that smoke is true, the alarm is always true regardless of fire is true or not. (Screen-off effect). In other words, fire and alarm are independent if conditioned on smoke.
A <– B –> C	Fork	Shoe Size <– Age of Child –> Reading Ability Children with large shoes tend to read at a higher level. But it is not a cause and effect relationship. Conditioning on Age of Child, Shoe Size, and Reading Ability are independent.
A –> B <– C	Collider	Talent –> Celebrity <– Beauty Talent and Beauty are independent. However, conditioning on Celebrity, Talent, and Beauty are dependent. In fact, Talent and Beauty are negatively correlated. If someone is a celebrity, and he is talented. It is less likely that he is also handsome, and vice versa. (Explain-away effect)

The power of knowing the arrow patterns is that we can now verify our causal model by observing data alone, for example, conditioning on something and check if the other two are correlated.

The author points out three important implications. First, causal assumptions, i.e., the diagram we draw, cannot be invented at our whim. They can be falsified using data. Second, the arrow pattern in the diagram dictates which causal models can be distinguished by data and which will forever remain indistinguishable. For example, you cannot distinguish between a fork and a chain using data alone. Conditioning on B, A, and C are always independent. Third, a casual diagram allows us to emulate interventions by observations on data. For example, consider a fork pattern. If we are able to increase the shoe size of a child, we can confirm that it has no impact on reading ability. But, we sometimes cannot have this intervention. In that case, we can observe the data, I.e., conditioned on the age of the child, and confirm that shoe size and reading ability are independent. Then we can conclude shoe size has no impact on reading ability.

In the next post, we will discuss Randomized Controlled Trial (RCT) and its pros and cons in its effort to address causation.