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Definition of Hidden Markov Model

The Hidden Markov Model is a finite set of states, each of which is associated with a (generally multidimensional) probability distribution []. Transitions among the states are governed by a set of probabilities called transition probabilities. In a particular state an outcome or observation can be generated, according to the associated probability distribution. It is only the outcome, not the state visible to an external observer and therefore states are ``hidden'' to the outside; hence the name Hidden Markov Model.

In order to define an HMM completely, following elements are needed.

Therefore we can use the compact notation


to denote an HMM with discrete probability distributions, while


to denote one with continuous densities. .

Narada Warakagoda
Fri May 10 20:35:10 MET DST 1996

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