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Introduction to Hidden Semi-Markov Models
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    Obzherin, Yuriy E. Voropai, N. Senderov, S. Michalevich, A. and Guliev, H. 2018. Semi-Markov and hidden semi-Markov models of energy systems. E3S Web of Conferences, Vol. 58, Issue. , p. 02023.

    Bobrowski, A. 2018. Lord Kelvin and Andrey Andreyevich Markov in a Queue with Single Server. Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software", Vol. 11, Issue. 3, p. 29.

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 This book contains new results and previously unpublished material not available elsewhere.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


'… 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 Source: MathSciNet

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Aggoun, L., Elliott, R. (2004). Measure Theory and Filtering: Introduction with Applications. Cambridge University Press.
Barbu, V.S., Limnios, N. (2008). Semi-Markov Chains and Hidden Semi- Markov Models Towards Applications: their Use in Reliability Theory and DNA Analysis. Springer.
Bartlett, M.S. (1978). An Introduction to Stochastic Processes, third edition. Cambridge University Press.
Berchtold, A., Raftery, A.E. (2002). The mixture transition distribution model for high-order Markov chains and non-Gaussian time series. Statistical Science, 17 (3), 328–356.
Borodovsky, M., Ekisheva, S. (2006). Problems and Solutions in Biological Sequence Analysis. Cambridge University Press.
Bressler, Y. (1986). Two-filter formula for discrete-time non-linear Bayesian smoothing. Int J. Control, 43, 629–641.
Bulla, J. (2006). Application of Hidden Markov Models and Hidden Semi- Markov Models to Financial Time Series. PhD Thesis, Universität Göttingen.
Bulla, J., Bulla, I. (2006). Stylized facts of financial time series and hidden semi-Markov models. Computat. Stat. and Data Anal., 51, 2192–2209.
Bulla, J., Bulla, I., Nenadić, O. (2010). hsmm – An R package for analyzing hidden semi-Markov models. Computational Statistics and Data Analysis, 54, 611–619.
Burge, C. (1997). Identification of Genes in Human Genomic DNA. PhDThesis, Stanford University.
Burge, C., Karlin, S. (1997). Prediction of complete gene structures in human genomic DNA. J. Mol. Biol., 268, 78–94.
Chen, S.F., Goodman, J. (1996). An empirical study of smoothing techniques for language modeling. In Proc. 34th Annual General Meeting on Association for Computational Linguistics, 310–318.
Cristianini, N., Hahn, M.W. (2007). Introduction to Computational Genomics: a Case Studies Approach. Cambridge University Press.
Cinlar, E. (1975). Introduction to Stochastic Processes. Prentice–Hall.
Claviere, J.-M., Notredame, C. (2007). Bioinformatics for Dummies. Wiley.
Cohen, S.N., Elliott, R.J. (2015). Stochastic Calculus and Applications. Birkauser.
Cowan, R. (1991). Expected frequency of DNA patterns using Whittle's formula. J. Applied Probability 28, 886–892.
Dempster, A.P., Laird, N.M., Rubin, D.B. (1977). Maximum likelihood From incomplete data via the EM algorithm. J. Roy. Stat. Soc., Series B, 39(1), 1–38.
Deonier, R.C., Tavaré, S., Waterman, M.S. (2005). Computational Genome Analysis: an Introduction. Springer.
Devijver, P.A. (1985). Baum's forward–backward algorithm revisited. Pattern Recognition Letters, 3, 369–373.
Durbin, R., Eddy, S., Krogh, A., Mitchison, G. (1998). Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids. Cambridge University Press.
Durrett, R. (2008). Probability Models for DNA Sequence Evolution. Springer.
Elliott, R.J., Aggoun, L., Moore, J.B. (1995). Hidden Markov Models: Estimation and Control. Springer.
Ewens, W.J., Grant G.R. (2010). Statistical Methods in Bioinformatics: an Introduction. Springer.
Ferguson, J.D. (1980). Variable duration models for speech. In Symposium on the Application of Hidden Markov Models to Text and Speech, Institute for Defense Analyses, Princeton, NJ. pp. 143–179.
Fink, G.A. (2008). Markov Models for Pattern Recognition: from Theory to Applications, second edition. Springer.
Guédon, Y. (1992). Review of several stochastic speech unit models. Computer Speech and Language, 6, 377–402.
Guédon, Y. (1999). Computational methods for discrete hidden semi-Markov chains. Applied Stochastic Models in Business and Industry, 15, 195–224.
Guédon, Y. (2003). Estimating hidden semi-Markov chains from discrete sequences. Computer Speech and Language, 12, 604–639.
Guédon, Y. (2004). Exploring the state sequence space for hidden Markov and semi-Markov chains. Computer Speech and Language, 51, 2379–2409.
Guédon, Y., Cocozza-Thivent, C. (1990). Explicit state occupancy modelling by hidden semi-Markov models: application of Derin's scheme. Computer Speech and Language, 4, 167–192.
Gusfield, D. (1997). Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology. Cambridge University Press.
Harlamov, B. (2008). Continuous Semi-Markov Processes. Wiley.
Howard, R.A. (1971). Dynamic Probabilistic Systems. Volume II: Semi- Markov and Decision Processes. Wiley.
Ignatova, Z., Martınez-Pérez, I., Zimmermann, K.-H. (2008). DNA Computing Models. Springer.
Isaev, A. (2006). Introduction to Mathematical Methods in Bioinformatics. Springer.
Janssen, J., Manca, R. (2010). Semi-Markov Risk Models for Finance, Insurance and Reliability. Springer.
Jelinek, F. (1997). Statistical Methods for Speech Recognition. MIT Press.
Jelinek, F., Mercer, R.L. (1980). Interpolated estimation of Markov source parameters from sparse data. In Pattern Recognition in Practice, Gelsema, E.S., Kanal, L.N. (eds.), pp. 381–397. North-Holland.
Jones, N.C., Pevzner, P.A. (2004). An Introduction to Bioinformatics Algorithms. MIT Press.
Kelly, F.P. (1982). Markovian functions of a Markov chain. Sankhya, 44 372–379.
Koski, T. (2001). Hidden Markov Models for Bioinformatics. Kluwer Academic.
Krishnamurthy, V., Moore, J.B., Chung, S.-H. (1991). On hidden fractal model signal processing. Signal Processing, 24, 177–192.
Levinson, S.E. (1986a). Continuously variable duration hidden Markov models for speech analysis. In Proceedings ICASSP, Tokyo, 1241–1244.
Levinson, S.E. (1986b). Continuously variable duration hidden Markov models for automatic speech recognition. Computer Speech and Language, 1, 29–45.
McLachlan, G.J., Peel, D. (2000). Finite Mixture Models. Wiley.
McLachlan, G.J., Krishnan, T. (2008). The EM Algorithm and its Extensions, second edition. Wiley.
Oksendal, B. (2010). Stochastic Differential Equations, 6th edition. Springer.
Pardoux, E. (2008). Markov Processes and Applications: Algorithms, Networks, Genomes and Finance. Wiley.
Pevsner, J. (2003). Bioinformatics and Functional Genomics. Wiley.
Prum, B, Rodolphe, F., Turckheim, E. (1995). Finding words with unexpected frequencies in DNA sequences. J. Royal Stat. Soc. Series B, 57, 205–220.
Rabiner, L.R. (1989). A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE, 77 (2), 257–287.
Rabiner, L., Juang, B.-H. (1993). Fundamentals of Speech Recognition. Prentice–Hall.
Raftery, A.E. (1985). A model for high-order Markov chains. J. Royal Stat. Soc. Series B, 47(3), 528–539.
Raftery, A.E., Tavare, S. (1994). Estimation and modelling repeated patterns in high-order Markov chains with the mixture transition distribution model. Applied Statistics, 43(1), 179–199.
Ramesh, R., Wilpon, J.G. (1992). Modeling state durations in hidden Markov models for automatic speech recognition. In: IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP-92, volume 1, pp. 381–384.
Reinart, G., Schbath, S., Waterman, M. (2000). Probabilistic and statistical properties of words: an overview. J. of Computational Biology, 7, 1–46.
Robin, S., Daubin, J.J. (1999). Exact distribution of word occurrences in a random sequence of letters. J. Applied Probability, 36, 179–193.
Robin, S., Rodolphe, F., Schbath, S. (2005). DNA, Words and Models: Statistics of Exceptional Words. Cambridge University Press.
Shmulevich, I., Dougher, E.R. (2007). Genomic Signal Processing. Princeton University Press.
Steeb, W.-H., Hardy, Y. (2011). Matrix Calculus and Kronecker Product: a Practical Approach to Linear and Multilinear Algebra, Second edition. World Scientific.
van der Hoek, J, Elliott, R.J. (2013). A modified hidden Markov model. Automatica, 49, 3509–3519.
Wall, J.E., Willsky, A.S., Sandell, N.R. (1981). On the fixed interval smoothing problem. Stochastics, 5, 1–42.
Waterman, M.S. (2000). Introduction to Computational Biology. Chapman and Hall/CRC.
Yu, S.-Z. (2010). Hidden semi-Markov models. Artificial Intelligence, 174, 215–243.
Yu, S.-Z., Kobayashi, H. (2003a). An explicit forward–backward algorithm for an explicit-duration hidden Markov model. IEEE Signal Processing Letters, 10, 11–14.
Yu, S.-Z., Kobayashi, H. (2003b). A hidden semi-Markov model with missing data and multiple observation sequences for mobility tracking. Signal Processing, 83, 235–250.
Yu, S.-Z., Kobayashi, H. (2006). Practical implemenation of an efficient forward–backward algorithm for an explicit-duration hidden Markov model. IEEE Transactions on Signal Processing, 54, 1947–1951.
Zucchini, W., MacDonald, I.L. (2009). Hidden Markov Models for Time Series: an Introduction using R. Chapman and Hall/CRC.


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