Introduction to Hidden Semi-Markov Models London Mathematical Society Lecture Note Series

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 This book contains new results and previously unpublished material not available elsewhere.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.

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 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).