UID:
almafu_9960117763502883
Format:
1 online resource (x, 174 pages) :
,
digital, PDF file(s).
Edition:
1st ed.
ISBN:
1-108-38198-7
,
1-108-38390-4
,
1-108-37742-4
Series Statement:
London Mathematical Society lecture note series ; 445
Content:
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 This book contains new results and previously unpublished material not available elsewhere.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.
Note:
Title from publisher's bibliographic system (viewed on 12 Feb 2018).
,
Cover -- Series page -- Title page -- Copyright page -- Contents -- Preface -- 1 Observed Markov Chains -- 1.1 Introduction -- 1.2 Observed Markov chain models -- 1.3 Notation -- 1.4 Construction of Markov chains -- 1.5 The general Markov chain -- 1.6 Conclusion -- 1.7 Exercises -- 2 Estimation of an Observed Markov Chain -- 2.1 Introduction -- 2.2 Estimation based on one sample path -- 2.3 Estimation using K sample paths of length L -- 2.4 Markov chains of order M ≥2 -- 2.5 Exercises -- 3 Hidden Markov Models -- 3.1 Definitions -- 3.2 Calculation of the likelihood -- 3.3 Exercises -- 4 Filters and Smoothers -- 4.1 Introduction -- 4.2 Decoding -- 4.3 Further remarks on filters and smoothers -- 4.4 Exercises -- 5 The Viterbi Algorithm -- 5.1 Introduction -- 5.2 Viterbi decoding -- 5.3 Estimation of the model -- 5.4 Exercises -- 6 The EM Algorithm -- 6.1 Introduction -- 6.2 Steps of the EM algorithm -- 6.3 Exercises -- 7 A New Markov Chain Model -- 7.1 Introduction -- 7.2 Construction of the model -- 7.3 Filters -- 7.4 Smoothers -- 7.5 The Viterbi algorithm -- 7.6 Parameter estimation by the EM algorithm -- 7.7 Steps of the EM algorithm -- 7.8 Exercises -- 8 Semi-Markov Models -- 8.1 Introduction -- 8.2 Semi-Markov models -- 8.3 Transition probabilities for semi-Markov chains -- 8.4 Exercises -- 9 Hidden Semi-Markov Models -- 9.1 Introduction -- 9.2 A semi-martingale representation for a semi-Markov chain -- 9.3 Construction of the semi-Markov model -- 9.4 Hidden semi-Markov models -- 9.5 Exercises -- 10 Filters for Hidden Semi-Markov Models -- 10.1 Introduction -- 10.2 The Viterbi algorithm -- 10.3 Smoothers -- 10.4 EM algorithm for estimating a hidden semi-Markov model -- 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.
Additional Edition:
ISBN 1-108-44198-X
Additional Edition:
ISBN 1-108-42160-1
Language:
English
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