Bayesian Networks (BNs)

Given some distribution \(\mathbb{P}\) over random variables \(\mathbf{V}\) and a Directed Acyclic Graph (DAG) \(G = (\mathbf{V},\mathbf{E})\), the pair \((G,\mathbb{P})\) is a Bayesian Network (BN) if \((G,\mathbb{P})\) satisfy the Markov Condition, i.e. for each \(V \in \mathbf{V}\) we have that it is independent of its non-descendants given its parents.

BNs are a graphical representation of conditional independence.