Hidden Markov Models

A hidden Markov model is a mathematical formalism that allows modeling of a stochastic system, which may undergo characteristic changes at uncertain times. It is often called a doubly stochastic process in which a Markov chain governs the characteristic change of the system and each state of the Markov chain is associated with a stochasitc process or distribution, which supports the random nature of the observation. It is thus also referred to a s probabilistic functions of Markov processes. In this article, we define this stochastic modeling technique, elaborate its key problems and solutions, and showm as a simple example, how this techniwue can be applied to real-world problems such as automatic speech recognition for communication services.