Editing Hidden Markov model (section)

==== Most likely explanation ====
The task, unlike the previous two, asks about the [[joint probability]] of the ''entire'' sequence of hidden states that generated a particular sequence of observations (see illustration on the right). This task is generally applicable when HMM's are applied to different sorts of problems from those for which the tasks of filtering and smoothing are applicable. An example is [[part-of-speech tagging]], where the hidden states represent the underlying [[Part-of-speech tagging|parts of speech]] corresponding to an observed sequence of words. In this case, what is of interest is the entire sequence of parts of speech, rather than simply the part of speech for a single word, as filtering or smoothing would compute.

This task requires finding a maximum over all possible state sequences, and can be solved efficiently by the [[Viterbi algorithm]].