Inference in Hidden Markov Models
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BeschreibungThis book is a comprehensive treatment of inference for hidden Markov models, including both algorithms and statistical theory. Topics range from filtering and smoothing of the hidden Markov chain to parameter estimation, Bayesian methods and estimation of the number of states. In a unified way the book covers both models with finite state spaces and models with continuous state spaces (also called state-space models) requiring approximate simulation-based algorithms that are also described in detail. Many examples illustrate the algorithms and theory. This book builds on recent developments to present a self-contained view.
InhaltsverzeichnisMain Definitions and Notations.- Main Definitions and Notations.- State Inference.- Filtering and Smoothing Recursions.- Advanced Topics in Smoothing.- Applications of Smoothing.- Monte Carlo Methods.- Sequential Monte Carlo Methods.- Advanced Topics in Sequential Monte Carlo.- Analysis of Sequential Monte Carlo Methods.- Parameter Inference.- Maximum Likelihood Inference, Part I: Optimization Through Exact Smoothing.- Maximum Likelihood Inference, Part II: Monte Carlo Optimization.- Statistical Properties of the Maximum Likelihood Estimator.- Fully Bayesian Approaches.- Background and Complements.- Elements of Markov Chain Theory.- An Information-Theoretic Perspective on Order Estimation.
PressestimmenFrom the reviews:
"By providing an overall survey of results obtained so far in a very readable manner, and also presenting some new ideas, this well-written book will appeal to academic researchers in the field of HMMs, with PhD students working on related topics included. It will also appeal to practitioners and researchers from other fields by guiding them through the computational steps needed for making inference HMMs and/or by providing them with the relevant underlying statistical theory. In the reviewer's opinion this book will shortly become a reference work in its field." MathSciNet
"This monograph is a valuable resource. It provides a good literature review, an excellent account of the state of the art research on the necessary theory and algorithms, and ample illustrations of numerous applications of HMM. It goes much beyond the earlier resources on HMM...I anticipate this work to serve well many Technometrics readers in the coming years." Haikady N. Nagaraja for Technometrics, November 2006
"This monograph is an attempt to present a reasonably complete up-to-date picture of the field of Hidden Markov Models (HMM) that is self-contained from a theoretical point of view and self sufficient from a methodological point of view. ... The book is written for academic researchers in the field of HMMs, and also for practitioners and researchers from other fields. ... all the theory is illustrated with relevant running examples. This voluminous book has indeed the potential to become a standard text on HMM." (R. Schlittgen, Zentralblatt MATH, Vol. 1080, 2006)
"Providing an overall survey of results obtained so far in a very readable manner ... this well-written book will appeal to academic researchers in the field of HMMs, with PhD students working on related topics included. It will also appeal to practitioners and researchers from other fields by guiding them through the computational steps needed for making interference on HMMs and/or by providing them with the relevant underlying statistical theory. In the reviewer's opinion this book will shortly become a reference work in its field." (M. Iosifescu, Mathematical Reviews, Issue 2006 e)
"The authors describe Hidden Markov Models (HMMs) as 'one of the most successful statistical modelling ideas ... in the last forty years.' The book considers both finite and infinite sample spaces. ... Illustrative examples ... recur throughout the book. ... This fascinating book offers new insights into the theory and application of HMMs, and in addition it is a useful source of reference for the wide range of topics considered." (B. J. T. Morgan, Short Book Reviews, Vol. 26 (2), 2006)
"In Inference in Hidden Markov Models, Cappé et al. present the current state of the art in HMMs in an emminently readable, thorough, and useful way. This is a very well-written book ... . The writing is clear and concise. ... the book will appeal to academic researchers in the field of HMMs, in particular PhD students working on related topics, by summing up the results obtained so far and presenting some new ideas ... ." (Robert Shearer, Interfaces, Vol. 37 (2), 2007)
Untertitel: 'Springer Series in Statistics'. 2005. Corr. 2nd. Sprache: Englisch.
Verlag: SPRINGER VERLAG GMBH
Erscheinungsdatum: Januar 2007
Seitenanzahl: 653 Seiten