Q1: in properties S1 ind. of S2 given S3, the S1 and S2 should be non-empty. Since the X1,X2,X3 are completely symmetric in this example, if you say that X1 and X2 are independent, that also means that X2 and X3 are independent etc.

]]>I'm confused about the definition of Id-sep(G).

If we take s={i}, than xi_x[n]\{i}|xi ( and so Xi_X{not s}|Xs) in Idsep, since Xi is in s, contained in any path from it, and does not in v-structure.

If so, it also looked like a minimal MB, which I guess it's notâ€¦.

I guess the definition of d-separating is missing:

X,Y are d-separated by Z in V\{X,Y}. (As written in some articles)

Moreover, I think there is a mistake at the notes page 5:

X_Y|Z in IdsepG if every path is not active regard to Z, which means it either has a node in Z that is not in a v structure or it has a node outside of Z that is in v-structure and *all its descendants are out of Z*

(The negation of the active path definition)

Q1:

About Iq CI- which r basically 3 groups of variables X,Y,Z.

Any of them can be empty? (Or just the condition part?)

Can them contain the same variables?

If so, there r 8 subsets of {1,2,3}, Wich means 8 options of each subset at the CI triple => 512 optionsâ€¦

(Maybe 256 if we consider there is no order between the 2 independent subset)

Should we ignore cases like X1_X2|X1,X3….? How many options should we check?

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