Q3:
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 not….
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 options…
(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?