INTRODUCTION
Hidden Markov models (HMMs) constitute a family of versatile statistical models that have proven useful in many applications. HMMs were introduced in their full generality in 1966 by Baum and Petrie (Baum and Petrie, 1966; Baum et al., 1970). Baum, Petrie and other colleagues at the Institute for Defense Analysis also developed and analyzed a maximum likelihood (ML) procedure for efficient estimation of the HMM parameters from a training sequence. This procedure turned out to be an instance of the now well known EM (Expectation-Maximization) algorithm of Dempster, Laird and Rubin (1977). A form of HMM, referred to as a Markov Source, was introduced as early as 1948 by Shannon in developing a model for the English language (Shannon, 1948).
Baum et al. (1970)referred to HMMs as probabilistic functions of Markov chains. Indeed, an HMM process comprises a Markov chain whose states are associated with some probability distributions. For example, the Markov states may be...
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Baum, L.E. and Petrie, T. (1966). “Statistical inference for probabilistic functions of finite state Markov chains,” Ann. Math. Statist., 37, 1554–1563.
Baum, L.E., Petrie, T., Soules, G., and Weiss, N. (1970). “A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains,” Ann. Math. Statist., 41, 164–171.
Couvreur, C. (1996). Hidden Markov Models and Their Mixtures, Department of Mathematics, Université Catholique de Louvain, Belgium [http://thor.fpms.ac.be/~couvreur/listpub.html].
Dempster, A.P., Laird, N.M., and Rubin, D.B. (1977). “Maximum likelihood from incomplete data via the EM algorithm,” Jl. Royal Stat. Soc. B, 39, 1–38.
Ferguson, J.D., editor (1980). Proc. of the Symposium on the applications of hidden Markov models to text and speech. IDA-CRD, Princeton, New Jersey.
Grimmett, G.R. and Stirzaker, D.R. (1995). Probability and Random Processes. Oxford Science Publications, Oxford, UK.
Jelinek, F. (1974). “Continuous speech recognition by statistical methods,” Proc. IEEE, 64, 532–556.
Leroux, B.G. (1992). “Maximum likelihood estimation for hidden Markov models,” Stochastic Processes and Their Applications, 40, 127–143.
Rabiner, L.R. (1989). “A tutorial on hidden Markov models and selected applications in speech recognition,” Proc. IEEE, 257–286.
Shannon, C.E. (1948). “A mathematical theory of communication,” Bell Syst. Tech. Jl., 27, 379–423, 623–656.
Wu, C.F.J. (1983). “On the convergence properties of the EM algorithm, Ann. Statist., 11, 95–103.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Kluwer Academic Publishers
About this entry
Cite this entry
Ephraim, Y. (2001). Hidden Markov models . In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_417
Download citation
DOI: https://doi.org/10.1007/1-4020-0611-X_417
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-7923-7827-3
Online ISBN: 978-1-4020-0611-1
eBook Packages: Springer Book Archive