Inference in Hidden Markov Models

By: Eric Moulines, Tobias Ryden, Olivier Cappe

Write A Review

Hardcover | 1 August 2005

At a Glance

Hardcover
676 Pages

Dimensions(cm)
24.2 x 15.8 x 4.2

Hardcover

$379.01

or 4 interest-free payments of $94.75 with

Ships in 5 to 7 business days

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.

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

Industry Reviews

From the reviews:

"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 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, Cappe 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)

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $0.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Mathematics Probability & Statistics Applied Mathematics Mathematical Modelling Engineering & Technology Electronics & Communications Engineering Communications Engineering & Telecommunications Economics Econometrics Economic Statistics Electronics Engineering

Computing & I.T.Graphical & Digital Media Applications 3D Graphics & Modelling

Preface	p. V
Contributors	p. IX
Introduction	p. 1
What Is a Hidden Markov Model?	p. 1
Beyond Hidden Markov Models	p. 4
Examples	p. 6
Finite Hidden Markov Models	p. 6
Normal Hidden Markov Models	p. 13
Gaussian Linear State-Space Models	p. 15
Conditionally Gaussian Linear State-Space Models	p. 17
General (Continuous) State-Space HMMs	p. 24
Switching Processes with Markov Regime	p. 29
Left-to-Right and Ergodic Hidden Markov Models	p. 33
Main Definitions and Notations	p. 35
Markov Chains	p. 35
Transition Kernels	p. 35
Homogeneous Markov Chains	p. 37
Non-homogeneous Markov Chains	p. 40
Hidden Markov Models	p. 42
Definitions and Notations	p. 42
Conditional Independence in Hidden Markov Models	p. 44
Hierarchical Hidden Markov Models	p. 46
State Inference
Filtering and Smoothing Recursions	p. 51
Basic Notations and Definitions	p. 53
Likelihood	p. 53
Smoothing	p. 54
The Forward-Backward Decomposition	p. 56
Implicit Conditioning (Please Read This Section!)	p. 58
Forward-Backward	p. 59
The Forward-Backward Recursions	p. 59
Filtering and Normalized Recursion	p. 61
Markovian Decompositions	p. 66
Forward Decomposition	p. 66
Backward Decomposition	p. 70
Complements	p. 74
Advanced Topics in Smoothing	p. 77
Recursive Computation of Smoothed Functionals	p. 77
Fixed Point Smoothing	p. 78
Recursive Smoothers for General Functionals	p. 79
Comparison with Forward-Backward Smoothing	p. 82
Filtering and Smoothing in More General Models	p. 85
Smoothing in Markov-switching Models	p. 86
Smoothing in Partially Observed Markov Chains	p. 86
Marginal Smoothing in Hierarchical HMMs	p. 87
Forgetting of the Initial Condition	p. 89
Total Variation	p. 90
Lipshitz Contraction for Transition Kernels	p. 95
The Doeblin Condition and Uniform Ergodicity	p. 97
Forgetting Properties	p. 100
Uniform Forgetting Under Strong Mixing Conditions	p. 105
Forgetting Under Alternative Conditions	p. 110
Applications of Smoothing	p. 121
Models with Finite State Space	p. 121
Smoothing	p. 122
Maximum a Posteriori Sequence Estimation	p. 125
Gaussian Linear State-Space Models	p. 127
Filtering and Backward Markovian Smoothing	p. 127
Linear Prediction Interpretation	p. 131
The Prediction and Filtering Recursions Revisited	p. 137
Disturbance Smoothing	p. 143
The Backward Recursion and the Two-Filter Formula	p. 148
Application to Marginal Filtering and Smoothing in CGLSSMs	p. 155
Monte Carlo Methods	p. 161
Basic Monte Carlo Methods	p. 161
Monte Carlo Integration	p. 162
Monte Carlo Simulation for HMM State Inference	p. 163
A Markov Chain Monte Carlo Primer	p. 166
The Accept-Reject Algorithm	p. 166
Markov Chain Monte Carlo	p. 170
Metropolis-Hastings	p. 171
Hybrid Algorithms	p. 179
Gibbs Sampling	p. 180
Stopping an MCMC Algorithm	p. 185
Applications to Hidden Markov Models	p. 186
Generic Sampling Strategies	p. 186
Gibbs Sampling in CGLSSMs	p. 194
Sequential Monte Carlo Methods	p. 209
Importance Sampling and Resampling	p. 210
Importance Sampling	p. 210
Sampling Importance Resampling	p. 211
Sequential Importance Sampling	p. 214
Sequential Implementation for HMMs	p. 214
Choice of the Instrumental Kernel	p. 218
Sequential Improtance Sampling with Resampling	p. 231
Weight Degeneracy	p. 231
Resampling	p. 236
Complements	p. 242
Implementation of Multinomial Resampling	p. 242
Alternatives to Multinomial Resampling	p. 244
Advanced Topics in Sequential Monte Carlo	p. 251
Alternatives to SISR	p. 251
I.I.D. Sampling	p. 253
Two-Stage Sampling	p. 256
Interpretation with Auxiliary Variables	p. 260
Auxiliary Accept-Reject Sampling	p. 261
Markov Chain Monte Carlo Auxiliary Sampling	p. 263
Sequential Monte Carlo in Hierarchical HMMs	p. 264
Sequential Importance Sampling and Global Sampling	p. 265
Optimal Sampling	p. 267
Application to CGLSSMs	p. 274
Particle Approximation of Smoothing Functionals	p. 278
Analysis of Sequential Monte Carlo Methods	p. 287
Importance Sampling	p. 287
Unnormalized Importance Sampling	p. 287
Deviation Inequalities	p. 291
Self-normalized Importance Sampling Estimator	p. 293
Sampling Importance Resampling	p. 295
The Algorithm	p. 295
Definitions and Notations	p. 297
Weighting and Resampling	p. 300
Application to the Single-Stage SIR Algorithm	p. 307
Single-Step Analysis of SMC Methods	p. 311
Mutation Step	p. 311
Description of Algorithms	p. 315
Analysis of the Mutation/Selection Algorithm	p. 319
Analysis of the Selection/Mutation Algorithm	p. 320
Sequential Monte Carlo Methods	p. 321
SISR	p. 321
I.I.D. Sampling	p. 324
Complements	p. 333
Weak Limits Theorems for Triangular Array	p. 333
Bibliographic Notes	p. 342
Parameter Inference
Maximum Likelihood Inference, Part I: Optimization Through Exact Smoothing	p. 347
Likelihood Optimization in Incomplete Data Models	p. 347
Problem Statement and Notations	p. 348
The Expectation-Maximization Algorithm	p. 349
Gradient-based Methods	p. 353
Pros and Cons of Gradient-based Methods	p. 358
Application to HMMs	p. 359
Hidden Markov Models as Missing Data Models	p. 359
EM in HMMs	p. 360
Computing Derivatives	p. 362
Connection with the Sensitivity Equation Approach	p. 364
The Example of Normal Hidden Markov Models	p. 367
EM Parameter Update Formulas	p. 367
Estimation of the Initial Distribution	p. 370
Recursive Implementation of E-Step	p. 371
Computation of the Score and Observed Information	p. 374
The Example of Gaussian Linear State-Space Models	p. 384
The Intermediate Quantity of EM	p. 385
Recursive Implementation	p. 387
Complements	p. 389
Global Convergence of the EM Algorithm	p. 389
Rate of Convergence of EM	p. 392
Generalized EM Algorithms	p. 393
Bibliographic Notes	p. 394
Maximum Likelihood Inference, Part II: Monte Carlo Optimization	p. 397
Methods and Algorithms	p. 398
Monte Carlo EM	p. 398
Simulation Schedules	p. 403
Gradient-based Algorithms	p. 408
Interlude: Stochastic Approximation and the Robbins-Monro Approach	p. 411
Stochastic Gradient Algorithms	p. 412
Stochastic Approximation EM	p. 414
Stochastic EM	p. 416
Analysis of the MCEM Algorithm	p. 419
Convergence of Perturbed Dynamical Systems	p. 420
Convergence of the MCEM Algorithm	p. 423
Rate of Convergence of MCEM	p. 426
Analysis of Stochastic Approximation Algorithms	p. 429
Basic Results for Stochastic Approximation Algorithms	p. 429
Convergence of the Stochastic Gradient Algorithm	p. 431
Rate of Convergence of the Stochastic Gradient Algorithm	p. 432
Convergence of the SAEM Algorithm	p. 433
Complements	p. 435
Statistical Properties of the Maximum Likelihood Estimator	p. 441
A Primer on MLE Asymptotics	p. 442
Stationary Approximations	p. 443
Consistency	p. 446
Construction of the Stationary Conditional Log-likelihood	p. 446
The Contrast Function and Its Properties	p. 448
Identifiability	p. 450
Equivalence of Parameters	p. 451
Identifiability of Mixture Densities	p. 454
Application of Mixture Identifiability to Hidden Markov Models	p. 455
Asymptotic Normality of the Score and Convergence of the Observed Information	p. 457
The Score Function and Invoking the Fisher Identity	p. 457
Construction of the Stationary Conditional Score	p. 459
Weak Convergence of the Normalized Score	p. 464
Convergence of the Normalized Observed Information	p. 465
Asymptotics of the Maximum Likelihood Estimator	p. 465
Applications to Likelihood-based Tests	p. 466
Complements	p. 468
Fully Bayesian Approaches	p. 471
Parameter Estimation	p. 471
Bayesian Inference	p. 471
Prior Distributions for HMMs	p. 475
Non-identifiability and Label Switching	p. 478
MCMC Methods for Bayesian Inference	p. 481
Reversible Jump Methods	p. 488
Variable Dimension Models	p. 488
Green's Reversible Jump Algorithm	p. 490
Alternative Sampler Designs	p. 498
Alternatives to Reversible Jump MCMC	p. 500
Multiple Imputations Methods and Maximum a Posteriori	p. 501
Simulated Annealing	p. 502
The SAME Algorithm	p. 503
Background and Complements
Elements of Markov Chain Theory	p. 513
Chains on Countable State Spaces	p. 513
Irreducibility	p. 513
Recurrence and Transience	p. 514
Invariant Measures and Stationarity	p. 517
Ergodicity	p. 519
Chains on General State Spaces	p. 520
Irreducibility	p. 521
Recurrence and Transience	p. 523
Invariant Measures and Stationarity	p. 534
Ergodicity	p. 541
Geometric Ergodicity and Foster-Lyapunov Conditions	p. 548
Limit Theorems	p. 552
Applications to Hidden Markov Models	p. 556
Phi-irreducibility	p. 557
Atoms and Small Sets	p. 558
Recurrence and Positive Recurrence	p. 560
An Information-Theoretic Perspective on Order Estimation	p. 565
Model Order Identification: What Is It About?	p. 566
Order Estimation in Perspective	p. 567
Order Estimation and Composite Hypothesis Testing	p. 569
Code-based Identification	p. 571
Definitions	p. 571
Information Divergence Rates	p. 574
MDL Order Estimators in Bayesian Settings	p. 576
Strongly Consistent Penalized Maximum Likelihood Estimators for HMM Order Estimation	p. 577
Efficiency Issues	p. 580
Variations on Stein's Lemma	p. 581
Achieving Optimal Error Exponents	p. 584
Consistency of the BIC Estimator in the Markov Order Estimation Problem	p. 587
Some Martingale Tools	p. 589
The Martingale Approach	p. 591
The Union Bound Meets Martingale Inequalities	p. 592
Complements	p. 600
Appendices
Conditioning	p. 605
Probability and Topology Terminology and Notation	p. 605
Conditional Expectation	p. 606
Conditional Distribution	p. 611
Conditional Independence	p. 614
Linear Prediction	p. 617
Hilbert Spaces	p. 617
The Projection Theorem	p. 619
Notations	p. 621
Mathematical	p. 621
Probability	p. 622
Hidden Markov Models	p. 622
Sequential Monte Carlo	p. 624
References	p. 625
Index	p. 645
Table of Contents provided by Ingram. All Rights Reserved.

Inference in Hidden Markov Models

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Probability & Statistics

Statistics and Data Handling for Biologists

A Student's Guide

Statistics and Data Handling for Biologists

A Student's Guide

Recent Advances in Information Systems

Proceedings of the ICRAIS, Pointe aux Piments, Mauritius, 10-12 September 2025

Small Probabilities and High Stakes

Elements in Decision Theory and Philosophy

Small Probabilities and High Stakes

Elements in Decision Theory and Philosophy

Data Science and Social Research III

Epistemology, Methods, Technology, Applications, and Relation to Artificial Intelligence

The Maths Book

Big Ideas Simply Explained

Mathematics for Machine Learning

Applied Multivariate Statistical Analysis

Volume 1

Foundations of Statistics

Sampling Theory and Practice

Probability and Statistics for Science and Engineering

Practical Statistics

How the World Really Works

A Scientist's Guide to Our Past, Present, and Future

Hands-On Programming with R

Write Your Own Functions and Simulations

Fooled By Randomness

The Hidden Role of Chance in Life and in the Markets

Statistical Rethinking

2nd Edition - A Bayesian Course with Examples in R and STAN

The Art of Uncertainty

How to Navigate Chance, Ignorance, Risk and Luck

Simply Maths

DK Simply

Introduction to Medical Statistics

4th edition

Psychology Statistics For Dummies

For Dummies

Freakonomics

A Rogue Economist Explores the Hidden Side of Everything

Freakonomics Revised and Expanded Edition

A Rogue Economist Explores the Hidden Side of Everything

Causal Inference

What If

This product is categorised by