In the book: Bayesian Networks With Examples in R, the author shows three examples of d-separation:

He cites: enter image description here

Then, just a few lines below, the author uses the dsep function, which returns FALSE for one of the examples previously given!! enter image description here

Is this a mistake in the book? If not, what am I missing, why is his explanation so confusing?

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    $\begingroup$ I think the figure just tries to show the different types of connections and is not claiming that d-separation exists in all of the examples. On the top of page 23, the authors state clearly that A and S are only d-separated if we are not conditioning on E. The figure legend should probably be worded more clearly. $\endgroup$ – COOLSerdash Jan 23 '20 at 12:50
  • $\begingroup$ I agree with you, but just below 'figure 1.3' he says "some examples of d-separation covering...", so in a sense he is in fact claiming that d-separation exists in the three examples... $\endgroup$ – Chicago1988 Jan 23 '20 at 13:01

The legend is wrong (or very misleading), while the code snippet displays the correct output. In the third example, given $E$, the highlighted node in grey, $A$ and $S$ are not d-separated.

In this elementary configuration, $E$ is called a collider, and in a collider, conditioning on the common effect $E$ makes $A$ and $S$ dependent on each other. See for example this course p. 483.

  • $\begingroup$ Thanks, your example is clear, but then; why do you say "it is not a mistake"? The right-most figure is not d-separated; therefore the author claiming that the right-most is d-separated is a mistake from the author. $\endgroup$ – Chicago1988 Jan 23 '20 at 13:11
  • $\begingroup$ Edited, I was talking the code output $\endgroup$ – TheCG Jan 23 '20 at 13:45

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