Inference in Hidden Markov Models

Olivier Cappé, Eric Moulines - Collection Springer Series In Statistics

672 pages, parution le 31/01/2005

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Résumé

Hidden Markov models have become a widely used class of statistical models with applications in diverse areas such as communications engineering, bioinformatics, finance and many more. This 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, which allow for exact algorithms for filtering, estimation etc. and models with continuous state spaces (also called state-space models) requiring approximate simulation-based algorithms that are also described in detail. Simulation in hidden Markov models is addressed in five different chapters that cover both Markov chain Monte Carlo and sequential Monte Carlo approaches. Many examples illustrate the algorithms and theory. The book also carefully treats Gaussian linear state-space models and their extensions and it contains a chapter on general Markov chain theory and probabilistic aspects of hidden Markov models.

This volume will suit anybody with an interest in inference for stochastic processes, and it will be useful for researchers and practitioners in areas such as statistics, signal processing, communications engineering, control theory, econometrics, finance and more. The algorithmic parts of the book do not require an advanced mathematical background, while the more theoretical parts require knowledge of probability theory at the measure-theoretical level.

Written for: Researchers and PhD students

Sommaire

Main Definitions and Notations
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
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
- Elements of Markov Chain Theory
- An Information-Theoretic Perspective on Order Estimation.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Olivier Cappé, Eric Moulines
Collection	Springer Series In Statistics
Parution	31/01/2005
Nb. de pages	672
Format	16 x 24
Couverture	Relié
Poids	1075g
Intérieur	Noir et Blanc
EAN13	9780387402642
ISBN13	978-0-387-40264-2