Semi-Markov Chains and Hidden Semi-Markov Models toward Applications

Their use in Reliability and DNA Analysis

  • Nikolaos Limnios
  • Vlad Stefan Barbu
Part of the Lecture Notes in Statistics book series (LNS, volume 191)

Table of contents

  1. Front Matter
    Pages 1-11
  2. Vlad Barbu, Nikolaos Limnios
    Pages 1-16
  3. Vlad Barbu, Nikolaos Limnios
    Pages 1-25
  4. Vlad Barbu, Nikolaos Limnios
    Pages 1-32
  5. Vlad Barbu, Nikolaos Limnios
    Pages 1-25
  6. Vlad Barbu, Nikolaos Limnios
    Pages 1-30
  7. Vlad Barbu, Nikolaos Limnios
    Pages 1-48
  8. Back Matter
    Pages 1-45

About this book

Introduction

This book is concerned with the estimation of discrete-time semi-Markov and hidden semi-Markov processes. Semi-Markov processes are much more general and better adapted to applications than the Markov ones because sojourn times in any state can be arbitrarily distributed, as opposed to the geometrically distributed sojourn time in the Markov case. Another 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. It can also serve as a text for a six month research-oriented course at a Master or PhD level. The prerequisites are a background in probability theory and finite state space Markov chains.

Vlad Stefan Barbu is associate professor in statistics at the University of Rouen, France, Laboratory of Mathematics ‘Raphaël Salem.’ His research focuses basically on stochastic processes and associated statistical problems, with a particular interest in reliability and DNA analysis. He has published several papers in the field.

Nikolaos Limnios is a professor in Applied Mathematics at the University of Technology of Compiègne. His research interest concerns stochastic processes and statistics with application to reliability. He is the co-author of the books: Semi-Markov Processes and Reliability (Birkhäuser, 2001 with G. Oprisan) and Stochastic Systems in Merging Phase Space (World Scientific, 2005, with V.S. Koroliuk).

Keywords

DNA analysis EM algorithm Markov chain Markov model Markov process Probability theory bioinformatics estimation hidden semi-Markov model reliability semi-Markov chains

Authors and affiliations

  • Nikolaos Limnios
  • Vlad Stefan Barbu
  1. 1.Département Génie InformatiqueUniversité de Technologie de CompiègneCompiègneFrance
  2. 2.UMR 6085 CNRSUniversité de RouenSt.-Etienne du RouvrayFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-73173-5
  • Copyright Information Springer-Verlag New York 2008
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-73171-1
  • Online ISBN 978-0-387-73173-5
  • Series Print ISSN 0930-0325