Game 5

"Game 5 is just Game 4 with a little extra wrinkle. Now a second back-door path Xโ†Bโ†Cโ†’Y needs to be closed. If we close this path by controlling for B, then we open up the M-shaped path Xโ†Aโ†’Bโ†Cโ†’Y. To close that path, we must control for A or C as well. However, notice that we could just control for C alone; that would close the path Xโ†Bโ†Cโ†’Y and not affect the other path." (Pearl, p. 162)

Game 5 in BayesiaLab

Here we have the causal Bayesian network corresponding to Game 5:โ€‹

  • Select Main Menu > Analysis > Visual > Graph > Influence Paths to Target and see that there is a noncausal path that needs to be blocked.

  • You can block this path by fixing the probability distribution of variable C.

  • You can check if this proposed approach is correct by setting your evidence โ€” Fix Probabilities on C โ€” and then running the Influence Paths Analysis again.

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