Description: 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, 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 This book contains new results and previously unpublished material not available elsewhere.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]
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BIC Subject Area 1: Signal processing [UYS]
BIC Subject Area 2: Stochastics [PBWL]
BIC Subject Area 3: Probability & statistics [PBT]
BIC Subject Area 4: Finance [KFF]
Number of Pages: 184 Pages
Language: English
Publication Name: Introduction to Hidden Semi-Markov Models
Publisher: Cambridge University Press
Publication Year: 2018
Subject: Mathematics
Item Height: 227 mm
Item Weight: 290 g
Type: Textbook
Author: John Van Der Hoek, Robert J. Elliott
Series: London Mathematical Society Lecture Note Series
Item Width: 151 mm
Format: Paperback
