[lnajjffo] Correlation, causality, and Bayesian networks

There are four reasons why random variables X and Y may be statistically correlated.

X causes Y.  This corresponds to an arrow (directed path) from X to Y in a Bayesian network.

Y causes X. An arrow from Y to X.

There is a common cause of X and Y.  This corresponds to a caret ^ upside-down V structure in a Bayesian network, with the common cause node as a parent (ancestor) of X and Y.

There was selection bias such that only correlated values of X and Y were observed.  This corresponds to the famous V structure in a Bayesian network, with the vertex of the V (or descendant) observed, allowing influence to flow between X and Y which would otherwise be independent.