d-separation

variables $X$ and $Y$ are said to be $d$ -separated, if all paths from $X$ to $Y$ are blocked. A path may be blocked by a set of variables $S$ , if the path contains at least one arrow-emitting variable that is in $S$ or if the path contains at least one collider that is not in S and has no descendent in $S$ . A collider is defined as a variable on a path such that the path enters and leaves via arrow heads. $X$ and $Y$ are, therefore, $d$ -separated conditional on $S$ , if $S$ blocks all paths between $X$ and $Y$ . X and Y are marginally independent when S contains the null set

by Boris Sobolev/in /on June 07, 2012