Semi-Markov Chains and Hidden Semi-Markov Models toward Applications: Their Use in Reliability and DNA Analysis

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Springer Science & Business Media, Jan 7, 2009 - Mathematics - 226 pages

Here is a work that adds much to the sum of our knowledge in a key area of science today. It is concerned with the estimation of discrete-time semi-Markov and hidden semi-Markov processes. A unique feature of the book is the use of discrete time, especially useful in some specific applications where the time scale is intrinsically discrete. The models presented in the book are specifically adapted to reliability studies and DNA analysis. The book is mainly intended for applied probabilists and statisticians interested in semi-Markov chains theory, reliability and DNA analysis, and for theoretical oriented reliability and bioinformatics engineers.

 

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Contents

Introduction
1
DiscreteTime Renewal Processes
17
SemiMarkov Chains
42
Nonparametric Estimation for SemiMarkov Chains
75
Reliability Theory for DiscreteTime SemiMarkov Systems
101
Hidden SemiMarkov Model and Estimation
131
Lemmas for SemiMarkov Chains
179
Lemmas for Hidden SemiMarkov Chains
183
Some Proofs
185
Markov Chains
194
Miscellaneous
203
Notation
207
References
211
Index
221
Copyright

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About the author (2009)

Catherine Huber is an Emeritus professor at Universite de Paris Rene Descartes. Her research activity concerns nonparametric and semi-parametric theory of statistics and their applications in biology and medicine. She has several publications in particular in the field of survival analysis. She is the co-author and co-editor of several books in the above fields.

Nikolaos Limnios is a professor at the University of Technology of Compiegne. His research and teaching activities concern stochastic processes, statistical inference and their applications in particular in reliability and survival analysis. He is the co-author and co-editor of several books in the above fields.

Mounir Mesbah is a professor at the Universite Pierre et Marie Curie, Paris 6. His research and teaching activities concern statistics and its applications in health science and medicine (biostatistics). He is the co-author of several articles and co-editor of several books in the above fields.

Mikhail Nikulin is a professor at the Universite Victor Segalen, and a member of the Institute of Mathematics at Bordeaux. His research and teaching activities concern mathematical statistics and its applications in reliability and survival analysis. He is the co-author and co-editor of several books in the above fields.

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