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Look Inside Introduction to Hidden Semi-Markov Models

Introduction to Hidden Semi-Markov Models

$68.99 (P)

Part of London Mathematical Society Lecture Note Series

Authors:
John van der Hoek, University of South Australia
Robert J. Elliott, University of Calgary

Date Published: May 2018
availability: Available
format: Paperback
isbn: 9781108441988

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About the Authors

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 This book contains new results and previously unpublished material not available elsewhere.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.
- Presents the theory in a discrete time, finite state framework
- Readily accessible to senior undergraduate and first-year graduate students
- Contains a wealth of new and previously unpublished material
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Reviews & endorsements
'… this book is of interest to researchers attracted by hidden Markov and semi-Markov models. It covers probabilistic and statistical treatments of the considered topics, and introduces the reader … to possible applications, mainly in genomics. Hence, Ph.D. students and specialists in the area of hidden Markov processes are invited to consider this book as a reference in their activities.' Antonio Di Crescenzo, MathSciNet
‘… 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
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Product details
- Date Published: May 2018
- format: Paperback
- isbn: 9781108441988
- length: 184 pages
- dimensions: 227 x 151 x 11 mm
- weight: 0.29kg
- availability: Available
Table of Contents
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.
Look Inside
Authors
John van der Hoek, University of South Australia
John van der Hoek is an Associate Professor at the University of South Australia. He has authored papers in partial differential equations, free boundary value problems, numerical analysis, stochastic analysis, actuarial science and mathematical finance. With Robert Elliott he co-authored Binomial Methods in Finance.
Robert J. Elliott, University of Calgary
Robert J. Elliott is a Research Professor at the University of South Australia. Previously he held positions at universities around the world, including Yale, Oxford, Alberta, Calgary and Adelaide. He has authored nine books, including Mathematics of Financial Markets (2004, with P. E. Kopp) and Stochastic Calculus and Application (1982).