Inference in Hidden Markov Models

Main 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.

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. 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. Many examples illustrate the algorithms and theory. The book builds on recent developments, both at the foundational level and the computational level, to present a self-contained view.

From 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 neededfor making interference