Editing Bayesian network (section)

===Causal networks===
Although Bayesian networks are often used to represent [[causality|causal]] relationships, this need not be the case: a directed edge from ''u'' to ''v'' does not require that ''X<sub>v</sub>'' be causally dependent on ''X<sub>u</sub>''. This is demonstrated by the fact that Bayesian networks on the graphs:

:<math> a \rightarrow b \rightarrow c \qquad \text{and} \qquad a \leftarrow b \leftarrow c </math>

are equivalent: that is they impose exactly the same conditional independence requirements.

A causal network is a Bayesian network with the requirement that the relationships be causal. The additional semantics of causal networks specify that if a node ''X'' is actively caused to be in a given state ''x'' (an action written as do(''X''&nbsp;=&nbsp;''x'')), then the probability density function changes to that of the network obtained by cutting the links from the parents of ''X'' to ''X'', and setting ''X'' to the caused value ''x''.<ref name=pearl2000/> Using these semantics, the impact of external interventions from data obtained prior to intervention can be predicted.