Bookstore

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 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.

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.