Introduction to hidden semi-Markov models

Description

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 This book contains new results and previously unpublished material not available elsewhere.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  Read more... Abstract: Markov chains and hidden Markov chains have applications in many areas of engineering and genomics. This book provides a basic introduction to the subject, developing the theory of Markov and semi-Markov processes in an elementary discrete time, finite state framework suitable for senior undergraduates and graduates.  Read more... Content: 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.