 MCd-separation introduces the graphical notion of d-separation. As noted above, a path from X to Y is a sequence of variables \(\langle X = X_1 , \ldots ,X_k = Y\rangle\) such that for each \(X_i\), \(X_{i+1}\), there is either an arrow from \(X_i\) to \(X_{i+1}\)or an arrow from \(X_{i+1}\) to \(X_i\) in \(\bG\). A variable \(X_i , 1 \lt i \lt k\) is a collider on the path just in case there is an arrow from \(X_{i-1}\) to \(X_i\) and from \(X_{i+1}\) to \(X_i\). In other words, \(X_i\) is a collider just in case the arrows converge on \(X_i\) in the path. Let \(\bX, \bY\), and \(\bZ\) be disjoint subsets of \(\bV\). \(\bZ\) d-separates \(\bX\) and \(\bY\) just in case every path \(\langle X_1 , \ldots ,X_k\rangle\) from a variable in \(\bX\) to a variable in \(\bY\) contains at least one variable \(X_i\) such that either: (i) \(X_i\) is a collider, and no descendant of \(X_i\) (including \(X_i\) itself) is in \(\bZ\); or (ii) \(X_i\) is not a collider, and \(X_i\) is in \(\bZ\). Any path that meets this condition is said to be blocked by \(\bZ\). If \(\bZ\) does not d-separate \(\bX\) and \(\bY\), then \(\bX\) and \(\bY\) are d-connected by \(\bZ\).