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Introduction to Hidden Semi-Markov Models de John van der Hoek

Introduction to Hidden Semi-Markov Models

Autor John van der Hoek, Robert J. Elliott
en Limba Engleză Paperback – 8 mar 2019
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 This book contains new results and previously unpublished material not available elsewhere.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.
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Specificații

ISBN-13: 9781108441988
ISBN-10: 110844198X
Pagini: 186
Dimensiuni: 152 x 229 x 10 mm
Greutate: 0.28 kg
Editura: Cambridge University Press
Locul publicării:Cambridge, United Kingdom

Cuprins

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.

Recenzii

'… 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

Descriere

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