Bayesian networks

Bayesian networks are a type of graphical model that involve a directed acyclic graph structure. We often refer to the tail node of a directed edge in a graphical model as the parent and the head node as the child or descendant. In fact, we generalize this latter notion so that, if there is a path from node A to node B in the model, node B is a descendant of node A. We can distinguish the special case of node A connected to node B by saying that the latter is a direct descendant.

The parent relationship and the descendant relationship are mutually exclusive in a Bayesian network because it has no cycles. Bayesian networks have the distinguishing property that, given its parents, every node in the network is conditionally independent of all other nodes in the network that are not its descendants. This is sometimes referred to as the local Markov property. It is an important property because it means that we can easily factorize the joint probability function of all the...