D-Sep definition
D-SEP(X,Y | Z) = yes if you can derive the independence of X and Y given Z
from the independencies in MARKOV(G)
How to check for D seperation ?
D-SEP(X,Y | Z) = yes if ALL paths from X to Y are blocked.
a path from X to Y is BLOCKED given Z if
1) there EXISTS a V-strcuture where neither the bottom node nor its descendants are in Z
OR
2) there EXISTS a node in Z on the path from X to Y, that it IS NOT a bottom node of a V-structure.
equivalently one can say that
D-SEP(x,Y | Z) = yes
if no path from X to Y is
ACTIVE.
a path from X to Y is ACTIVE given Z if
1) in ALL V-structure in the path from X to Y the bottom node or one of its descendants are in Z
AND
2) there is NO OTHER EVIDENCE in the path.