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 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.[1][2] 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.[3] 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.
Statisticians are enormously interested in the ways in which certain events and variables are connected. The precise notion of what constitutes a cause and effect is necessary to understand the connections between them. The central idea behind the philosophical study of causation is that causes raise the probabilities of their effects, all else being equal.
A deterministic interpretation of causation means that if A causes B, then A must always be followed by B. In this sense, smoking does not cause cancer because some smokers never develop cancer.
On the other hand, a probabilistic interpretation simply means that causes raise the probability of their effects. In this sense, changes in meteorological readings associated with a storm do cause that storm, since they raise its probability. (However, simply looking at a barometer does not change the probability of the storm, for a more detailed analysis, see:[4]).
Implicationsedit
This section needs expansion. You can help by adding to it. (July 2019)
Dependence and Causationedit
It follows from the definition that if X and Y are in V and are probabilistically dependent, then either X causes Y, Y causes X, or X and Y are both effects of some common cause Z in V.[3] This definition was seminally introduced by Hans Reichenbach as the Common Cause Principle (CCP) [5]
Screeningedit
It once again follows from the definition that the parents of X screen X from other "indirect causes" of X (parents of Parents(X)) and other effects of Parents(X) which are not also effects of X.[3]
Examplesedit
In a simple view, releasing one's hand from a hammer causes the hammer to fall. However, doing so in outer space does not produce the same outcome, calling into question if releasing one's fingers from a hammer always causes it to fall.
A causal graph could be created to acknowledge that both the presence of gravity and the release of the hammer contribute to its falling. However, it would be very surprising if the surface underneath the hammer affected its falling. This essentially states the Causal Markov Condition, that given the existence of gravity the release of the hammer, it will fall regardless of what is beneath it.
^Geiger, Dan; Pearl, Judea (1990). "On the Logic of Causal Models". Machine Intelligence and Pattern Recognition. 9: 3–14. doi:10.1016/b978-0-444-88650-7.50006-8.
^Lauritzen, S. L.; Dawid, A. P.; Larsen, B. N.; Leimer, H.-G. (August 1990). "Independence properties of directed markov fields". Networks. 20 (5): 491–505. doi:10.1002/net.3230200503.
^ abcHausman, 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.
^Pearl, Judea (2009). Causality. Cambridge: Cambridge University Press. doi:10.1017/cbo9780511803161. ISBN9780511803161.
^Reichenbach, Hans (1956). The Direction of Time. Los Angeles: University of California Press. ISBN9780486409269.
November 02, 2023
causal, markov, condition, markov, condition, sometimes, called, markov, assumption, assumption, made, bayesian, probability, theory, that, every, node, bayesian, network, conditionally, independent, nondescendants, given, parents, stated, loosely, assumed, th. 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 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 1 2 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 3 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 Contents 1 Motivation 2 Implications 2 1 Dependence and Causation 2 2 Screening 3 Examples 4 See also 5 NotesMotivation editMain article Probabilistic causation Statisticians are enormously interested in the ways in which certain events and variables are connected The precise notion of what constitutes a cause and effect is necessary to understand the connections between them The central idea behind the philosophical study of causation is that causes raise the probabilities of their effects all else being equal A deterministic interpretation of causation means that if A causes B then A must always be followed by B In this sense smoking does not cause cancer because some smokers never develop cancer On the other hand a probabilistic interpretation simply means that causes raise the probability of their effects In this sense changes in meteorological readings associated with a storm do cause that storm since they raise its probability However simply looking at a barometer does not change the probability of the storm for a more detailed analysis see 4 Implications editThis section needs expansion You can help by adding to it July 2019 Dependence and Causation edit It follows from the definition that if X and Y are in V and are probabilistically dependent then either X causes Y Y causes X or X and Y are both effects of some common cause Z in V 3 This definition was seminally introduced by Hans Reichenbach as the Common Cause Principle CCP 5 Screening edit It once again follows from the definition that the parents of X screen X from other indirect causes of X parents of Parents X and other effects of Parents X which are not also effects of X 3 Examples editIn a simple view releasing one s hand from a hammer causes the hammer to fall However doing so in outer space does not produce the same outcome calling into question if releasing one s fingers from a hammer always causes it to fall A causal graph could be created to acknowledge that both the presence of gravity and the release of the hammer contribute to its falling However it would be very surprising if the surface underneath the hammer affected its falling This essentially states the Causal Markov Condition that given the existence of gravity the release of the hammer it will fall regardless of what is beneath it See also editCausal modelNotes edit Geiger Dan Pearl Judea 1990 On the Logic of Causal Models Machine Intelligence and Pattern Recognition 9 3 14 doi 10 1016 b978 0 444 88650 7 50006 8 Lauritzen S L Dawid A P Larsen B N Leimer H G August 1990 Independence properties of directed markov fields Networks 20 5 491 505 doi 10 1002 net 3230200503 a b c 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 Pearl Judea 2009 Causality Cambridge Cambridge University Press doi 10 1017 cbo9780511803161 ISBN 9780511803161 Reichenbach Hans 1956 The Direction of Time Los Angeles University of California Press ISBN 9780486409269 Retrieved from https en wikipedia org w index php title Causal Markov condition amp oldid 1175758633, wikipedia, wiki, book, books, library,
