The Mathematical Garden

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Mathematical methods
HMMs
Introduction
The HMM
Estimate alpha
Simulate a HMM
Estimation of alpha
Extension of the model
Summary and references
Mathematical Induction
Pigeonhole principle
Random Walk
Solving Linear Systems

Summary

We discussed a simple HMM via the framework of classical Markov chain model. A simple estimation method for the transition probabilities among the hidden states is given. We remark that the estimation method can be easily implemented in a spreadsheet environment such as EXCEL.

References

  1. W. Ching and M. Ng, Building Simple Hidden Markov Models, International Journal of Mathematical Education in science and Engineering (2004).
  2. V. Chvatal, Linear Programming, Freeman, New York (1983).
  3. T. Koski, Hidden Markov Models for Bioinformatics, Kluwer Academic Publisher, Dordrecht (2001).
  4. I. MacDonald and W. Zucchini, Hidden Markov and Other Models for Discrete-valued Time Series, Chapman & Hall, London (1997).
  5. L. Rabiner, A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition, Proceedings of the IEEE, 77 (1989) 257-286.
  6. M. Ross, Introduction to Probability Models, Academic Press, Eighth Edition, New York (2003).
Department of Mathematics, HKU, 2010