## Quick Reference

A graph in which nodes represent random variables. Pairs of nodes connected by arcs correspond to variables that are not independent of one another. If two sets of nodes *A* and *B* are not connected, except via paths that pass through a node in a third set, *C*, then the variables represented by the nodes in the set *A* are conditionally independent of the variables represented by the nodes in the set *B*, given the values of the variables represented by the nodes in the set *C*.

If an arc has no direction attached, then this implies that there is association but not causation. An undirected graphical model (also called a Markov random field) is a model in which no arcs have directions attached. A model in which all arcs have directions attached is called a directed graphical model (or Bayes network or Bayes net). If we consider a directed path as referring to ‘generations’ of variables, then a simple example of conditional independence (not the only possibility) occurs when a ‘child variable’ is conditionally independent of earlier ‘ancestor variables’, given the values of the ‘parent variables’. A special case is the hidden Markov model. A graph containing a mixture of directed and undirected arcs is a chain graph.

*Subjects:*
Probability and Statistics.

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