Introduction to Hidden Semi-Markov Models

Develops the theory of Markov and semi-Markov processes in an elementary setting suitable for senior undergraduate and graduate students.

John van der Hoek (Author), Robert J. Elliott (Author)

9781108441988, Cambridge University Press

Paperback / softback, published 8 February 2018

184 pages
22.7 x 15.1 x 1.1 cm, 0.29 kg

'… dedicated mostly to graduate students and providing a rigorous and rather complete mathematical introduction to the theory of hidden Markov models as well as hidden semi-Markov models under main assumption that the hidden process is a finite state Markov chain. The semi-Markov models appear when the assumption that the length of time the chain spends in any state is geometrically distributed is relaxed. The authors carefully construct these processes on the canonical probability space and then derive filters and smoother, as well as the Viterbi estimates. The central role plays the EM Algorithm.' Jerzy Ombach, ZB Math Reviews

Markov chains and hidden Markov chains have applications in many areas of engineering and genomics. This book provides a basic introduction to the subject by first developing the theory of Markov processes in an elementary discrete time, finite state framework suitable for senior undergraduates and graduates. The authors then introduce semi-Markov chains and hidden semi-Markov chains, before developing related estimation and filtering results. Genomics applications are modelled by discrete observations of these hidden semi-Markov chains. This book contains new results and previously unpublished material not available elsewhere. The approach is rigorous and focused on applications.

Preface
1. Observed Markov chains
2. Estimation of an observed Markov chain
3. Hidden Markov models
4. Filters and smoothers
5. The Viterbi algorithm
6. The EM algorithm
7. A new Markov chain model
8. Semi-Markov models
9. Hidden semi-Markov models
10. Filters for hidden semi-Markov models
Appendix A. Higher order chains
Appendix B. An example of a second order chain
Appendix C. A conditional Bayes theorem
Appendix D. On conditional expectations
Appendix E. Some molecular biology
Appendix F. Earlier applications of hidden Markov chain models
References
Index.

Subject Areas: Signal processing [UYS], Stochastics [PBWL], Probability & statistics [PBT], Finance [KFF]