A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition

II.A Extension to hidden Markov models

1. What is a hidden Markov model?
   A doubly embedded stochastic process: an underlying Markov chain of states that is not observable, seen only through another stochastic process that produces observations as a probabilistic function of the state.
   • Rabiner, 1989, A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition (Proceedings of the IEEE), II.A Extension to hidden Markov models
2. How does Rabiner’s coin-tossing example motivate HMMs, and what does it say about model size?
   Someone behind a curtain reports only heads and tails. One biased coin (1 parameter), two coins (4 parameters) or three coins (9 parameters) could explain the sequence. Bigger models are more expressive, but practical considerations limit size, and a 3-coin model is inappropriate if only one coin is really tossed.
   • Rabiner, 1989, A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition (Proceedings of the IEEE), II.A Extension to hidden Markov models
3. Describe the urn-and-ball model of an HMM.
   A genie picks an urn according to a random process, draws a coloured ball, records its colour and replaces it, then picks the next urn depending on the current one. We see only the colours: states are urns, observations are colours.
   • Rabiner, 1989, A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition (Proceedings of the IEEE), II.A Extension to hidden Markov models