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The simplest Markov model is the [[Markov chain]]. It models the state of a system with a [[random variable]] that changes through time. In this context, the Markov property suggests that the distribution for this variable depends only on the distribution of the previous state. An example use of a Markov chain is [[Markov Chain Monte Carlo]], which uses the Markov property to prove that a particular method for performing a random walk will sample from the joint distribution of a system.
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A [[hidden Markov model]] is a Markov chain for which the state is only partially observable. In other words, observations are related to the state of the system, but they are typically insufficient to precisely determine the state. Several well-known algorithms for hidden Markov models exist. For example, given a sequence of observations, the [[Viterbi algorithm]] will compute the most-likely corresponding sequence of states, the forward algorithm will compute the probability of the sequence of observations, and the [[Baum–Welch algorithm]] will estimate the starting probabilities, the transition function, and the observation function of a hidden Markov model. One common use of hidden Markov models is for voice recognition.
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