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In [[probability theory]], a '''Markov model''' is a stochastic model that assumes the [[Markov property]]. Generally, this assumption enables reasoning and computation with the model that would otherwise be [[Intractable#Intractability|intractable]].
==Introduction== The most common Markov models and their relationships are summarized in the following table: {| border="1"
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A [[Markov random field]] (also called a Markov network) may be considered to be a generalization of a Markov chain in multiple dimensions. In a Markov chain, state depends only on the previous state in time, whereas in a Markov random field, each state depends on its neighbors in any of multiple directions. A Markov random field may be visualized as a field or graph of random variables, where the distribution of each random variable depends on the neighboring variables with which it is connected. More specifically, the joint distribution for any random variable in the graph can be computed as the product of the "clique potentials" of all the cliques in the graph that contain that random variable. Modeling a problem as a Markov random field is useful because it implies that the joint distributions at each vertex in the graph may be computed in this manner.
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[[Category:Markov models]]
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