The Back-Door Criterion
Context
Causal effect estimation is the topic of Chapter 10 in our book, Bayesian Networks & BayesiaLab. In this context, we discuss the central role of confounders and non-confounders in identifying and estimating causal effects. Much of what we explain in that chapter is a practical illustration of Judea Pearl's teaching on causality.
As the originator of an entire school of thought on causality, Judea Pearl is certainly at liberty to take a more light-hearted and playful approach in presenting this serious topic. Chapter 4 in The Book of Why he titled "Confounding and Deconfounding: Or, Slaying the Lurking Variable." In fact, Pearl presents the task of "deconfounding" for causal effect estimation as a series of "games," which we now wish to illustrate with Bayesian networks.
The Back-Door Criterion and Deconfounding โ It's All Fun and Games
We begin with a selection of quotes from the beginning of Chapter 4 to provide motivation for the forthcoming examples.
"To understand the back-door criterion, it helps first to have an intuitive sense of how information flows in a causal diagram. I like to think of the links as pipes that convey information from a starting point X to a finish Y. Keep in mind that the conveying of information goes in both directions, causal and noncausal, as we saw in Chapter 3.
In fact, the noncausal paths are precisely the source of confounding."
"To deconfound two variables X and Y, we need only to block every noncausal path between them without blocking or perturbing any causal paths."
"With these rules, decounfounding becomes so simple and fun that you can treat it like a game"
For each of the proposed games in Chapter 4, we prepare a corresponding Bayesian network in BayesiaLab. These networks allow you to experiment with the "pipes that convey information" as if they were set up in a laboratory, where you can look inside the tubes and measure the flows in pipes:
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