Bayesian Network

A Bayesian network is a simple, graphical notation for conditional independence assertions => compact specification of full joint distributions.

• Each node corresponds to a random variable (discrete or continuous).
• Directed edge from node $u$ to node $v$ means $u$ is parent of $v$. Likewise, $v$ is the child.
• Graph is a Directed Acyclic Graph (no directed cycles).
• Each node $u$ has a conditional probability $P(u|\text{Parents}(u))$ that quantifies the effect of the parent nodes.