 Suppose, moreover, that we have a probability distribution \(\Pr'\) on \(\bU\) in which all of the \(U_i\)s are independent. This will induce a probability distribution P on \(\bV\) that satisfies MC relative to the correct causal DAG on \(\bV\). In other words, our probabilistic SEM will generate a unique causal Bayes net. The methods described in the previous section attempt to infer the underlying graph \(\bG\) from relations of probabilistic dependence and independence. These methods can do no better than identifying the Markov equivalence class. Can we do better by making use of additional information about the probability distribution P, beyond relations of dependence and independence?