Causal Markov condition

The Markov condition (sometimes called Markov assumption) for a Bayesian network states that any node in a Bayesian network is conditionally independent of its nondescendents, given its parents.

A node is conditionally independent of the entire network, given its Markov blanket.

The related causal Markov condition is that a phenomenon is independent of its noneffects, given its direct causes.^[1] 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.

Notes

1. Hausman, D.M.; Woodward, J. (December 1999). "Independence, Invariance, and the Causal Markov Condition" (PDF). British Journal for the Philosophy of Science. 50 (4): 521–583. doi:10.1093/bjps/50.4.521.