 It is relatively easy to see why this holds. For each variable \(X_i\), its parents must come from among the variables with lower time indices, call them \(X_1 ,\ldots ,X_{i-1}\). Any variables in this group that are not parents of \(X_i\) will be nondescendants of \(X_i\); hence they will be screened off from \(X_i\) by its parents (from MCScreening_off). Thus we can start with the distributions \(\Pr(X_i\mid X_1 ,\ldots ,X_{i-1})\), and then weed out any variables from the right hand side that make no difference to the probability distribution over \(X_i\). By the Minimality Condition, we know that the variables so weeded are not parents of \(X_i\). Those variables that remain are the parents of \(X_i\) in \(\bG\).