A hidden Markov model (HMM) is a statistical model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest dynamic Bayesian network.

In a regular Markov model, the state is directly visible to the observer, and therefore the state transition probabilities are the only parameters. In a hidden Markov model, the state is not directly visible, but output dependent on the state (observation) is visible. Each state has a probability distribution over the possible output tokens. Therefore the sequence of tokens generated by an HMM gives some information about the sequence of states. A hidden Markov model is defined with a set of states and the state transition probability distribution over them, a set of possible observations and the probability distribution of the observations for each state, and an initial state probability distribution. Note that the adjective 'hidden' refers to the state sequence through which the model passes, not to the parameters of the model; Even if the model parameters are known exactly, the model is still 'hidden'.

There are three problems regarding HMMs. First of all given a sequence of observations and a model we need to estimate the corresponding states of these observations (decoding problem) or more importantly the current state of the model. The second problem is to specify model parameters (initial probabilities, state transition probabilities, and observation probabilities) so that we could correctly detect the state sequence of the model (learning problem). And finally we need a criterion by which we could evaluate how accurate we have determined the model parameters that is given an observation sequence and a model, what is the probability that the sequence was generated by the model (evaluation problem). These problems have been addressed in more details in [1]

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Hidden Markov models are especially known for their application in temporal pattern recognition such as speech recognition, handwriting, gesture recognition, activity recognition in context-aware systems, part-of-speech tagging, musical score following, partial discharges and bioinformatics.