Inference in Hidden Markov Models

Olivier Cappé, Eric Moulines, Tobias Ryden0387402640, 9780387402642, 9780387289823

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.

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Table of contents :
front-matter……Page 1
1Introduction……Page 16
2Main Definitions and Notations……Page 50
3Filtering and Smoothing Recursions……Page 63
4Advanced Topics in Smoothing……Page 89
5Applications of Smoothing……Page 133
6Monte Carlo Methods……Page 172
7Sequential Monte Carlo Methods……Page 220
8Advanced Topics in Sequential Monte Carlo……Page 262
9Analysis of Sequential Monte Carlo Methods……Page 298
10Maximum Likelihood Inference, Part I Optimization Through Exact Smoothing……Page 355
11Maximum Likelihood Inference, Part II Monte Carlo Optimization……Page 404
12Statistical Properties of the Maximum Likelihood Estimator……Page 447
13Fully Bayesian Approaches……Page 476
14Elements of Markov Chain Theory……Page 516
15An Information-Theoretic Perspective on Order Estimation……Page 568
back-matter……Page 605