Editing Causal Markov condition (section)

The '''Markov condition''', sometimes called the '''Markov assumption''', is an assumption made in [[Bayesian probability theory]], that every node in a [[Bayesian network]] is [[conditionally independent]] of its nondescendants, given its parents. Stated loosely, it is assumed that a node has no bearing on nodes which do not descend from it. In a [[Directed acyclic graph|DAG]], this local Markov condition is equivalent to the global Markov condition, which states that [[Bayesian network#d-separation|d-separations]] in the graph also correspond to conditional independence relations.<ref>{{cite journal |last1=Geiger |first1=Dan |last2=Pearl |first2=Judea |title=On the Logic of Causal Models |journal=Machine Intelligence and Pattern Recognition |date=1990 |volume=9 |pages=3–14 |doi=10.1016/b978-0-444-88650-7.50006-8}}</ref><ref>{{cite journal |last1=Lauritzen |first1=S. L. |last2=Dawid |first2=A. P. |last3=Larsen |first3=B. N. |last4=Leimer |first4=H.-G. |title=Independence properties of directed markov fields |journal=Networks |date=August 1990 |volume=20 |issue=5 |pages=491–505 |doi=10.1002/net.3230200503}}</ref> This also means that a node is conditionally independent of the entire network, given its [[Markov blanket]].

The related '''Causal Markov (CM) condition''' states that, conditional on the set of all its direct causes, a node is independent of all variables which are not effects or direct causes of that node.<ref name=":0">{{cite journal |last1=Hausman |first1=D.M. |last2=Woodward |first2=J. |title=Independence, Invariance, and the Causal Markov Condition |journal=British Journal for the Philosophy of Science |volume=50 |issue=4 |pages=521–583 |date=December 1999 |doi= 10.1093/bjps/50.4.521|url=http://philosophy.wisc.edu/hausman/papers/bjps.pdf }}</ref> In the event that the structure of a Bayesian network accurately depicts [[causality]], the two conditions are equivalent. However, a network may accurately embody the Markov condition without depicting causality, in which case it should not be assumed to embody the causal Markov condition.