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{{main|Hidden Markov model}}
A [[hidden Markov model]] is a Markov chain for which the state is only partially observable or noisily 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 is for [[speech recognition]], where the observed data is the [[Speech coding|speech audio]] [[waveform]] and the hidden state is the spoken text. In this example, the Viterbi algorithm finds the most likely sequence of spoken words given the speech audio.
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