Markov Independence Assumption: Difference between revisions
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* (Wikipedia, 2021) ⇒ https://en.wikipedia.org/wiki/Causal_Markov_condition Retrieved:2021-5-25. | * (Wikipedia, 2021) ⇒ https://en.wikipedia.org/wiki/Causal_Markov_condition Retrieved:2021-5-25. | ||
** 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 nondescendents, 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- | ** 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 nondescendents, 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-separation]]s in the graph also correspond to conditional independence relations. 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 direct causes or direct effects of that node. 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. | ||
<references/> | <references/> | ||
Latest revision as of 07:32, 22 August 2024
A Markov Independence Assumption is a statistical modeling assumption that every node in a Bayesian network follows a Markov property (that they are conditionally independent of its nondescendents, given its parents).
- See: Causality, Bayesian Probability Theory, Bayesian Network, Conditionally Independent, Directed Acyclic Graph, Markov Blanket, Hidden Markov Model, Naive-Bayes Model, Statistical Independence Relation.
References
2021
- (Wikipedia, 2021) ⇒ https://en.wikipedia.org/wiki/Causal_Markov_condition Retrieved:2021-5-25.
- 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 nondescendents, given its parents. Stated loosely, it is assumed that a node has no bearing on nodes which do not descend from it. In a DAG, this local Markov condition is equivalent to the global Markov condition, which states that d-separations in the graph also correspond to conditional independence relations. 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 direct causes or direct effects of that node. 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.
2021
- (Wikipedia, 2021) ⇒ https://en.wikipedia.org/wiki/Markov_property Retrieved:2021-5-25.
- … The term Markov assumption is used to describe a model where the Markov property is assumed to hold, such as a hidden Markov model. A Markov random field extends this property to two or more dimensions or to random variables defined for an interconnected network of items.