Causal Markov condition

<p>The Markov condition, sometimes called the Markov assumption, is an assumption made in <a href="/facts/Bayesian_probability_theory/Cvn7WWfG">Bayesian probability theory</a>, that every node in a <a href="/facts/Bayesian_network/Ry31vq6T">Bayesian network</a> is <a href="/facts/Conditionally_independent/udUXFaMw">conditionally independent</a> 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 <a href="/facts/Directed_acyclic_graph/k6zq1os9">DAG</a>, this local Markov condition is equivalent to the global Markov condition, which states that <a href="/facts/Bayesian_network/Ry31vq6T">d-separations</a> in the graph also correspond to conditional independence relations. This also means that a node is conditionally independent of the entire network, given its <a href="/facts/Markov_blanket/h3Ns4Nhj">Markov blanket</a>.
</p><p>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. In the event that the structure of a Bayesian network accurately depicts <a href="/facts/Causality/Swh496X7">causality</a>, 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.
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Causal Markov condition open-in-new

Causal Markov condition