Sequential Monte Carlo Methods in Practice

By: Arnaud Doucet (Editor), A. Smith (Foreword by), Nando de Freitas (Editor)

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Hardcover | 21 June 2001

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Monte Carlo methods are revolutionizing the on-line analysis of data in fields as diverse as financial modeling, target tracking and computer vision. These methods, appearing under the names of bootstrap filters, condensation, optimal Monte Carlo filters, particle filters and survival of the fittest, have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection, computer vision, semiconductor design, population biology, dynamic Bayesian networks, and time series analysis. This will be of great value to students, researchers and practitioners, who have some basic knowledge of probability. Arnaud Doucet received the Ph. D. degree from the University of Paris-XI Orsay in 1997. From 1998 to 2000, he conducted research at the Signal Processing Group of Cambridge University, UK. He is currently an assistant professor at the Department of Electrical Engineering of Melbourne University, Australia. His research interests include Bayesian statistics, dynamic models and Monte Carlo methods. Nando de Freitas obtained a Ph.D. degree in information engineering from Cambridge University in 1999. He is presently a research associate with the artificial intelligence group of the University of California at Berkeley. His main research interests are in Bayesian statistics and the application of on-line and batch Monte Carlo methods to machine learning. Neil Gordon obtained a Ph.D. in Statistics from Imperial College, University of London in 1993. He is with the Pattern and Information Processing group at the Defence Evaluation and Research Agency in the United Kingdom. His research interests are in time series, statistical data analysis, and pattern recognition with a particular emphasis on target tracking and missile guidance.

Industry Reviews

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION

"...a remarkable, successful effort at making these ideas available to statisticians. It gives an overview, presents available theory, gives a splendid development of various bells and whistles important in practical implementation, and finally gives a large number of detailed examples and case studies...The authors and editors have been careful to write in a unified, readable way...I find it remarkable that the editors and authors have combined to produce an accessible bible that will be studied and used for years to come."

"Usually, very few volumes edited from papers contributed by many different authors result in books which can serve as either good textbooks or as useful reference. However, in the case of this book, it is enough to read the foreword by Adrian Smith to realize that this particular volume is quite different. ... it is a good reference book for SMC." (Mohan Delampady, Sankhya: Indian Journal of Statistics, Vol. 64 (A), 2002)

"In this book the authors present sequential Monte Carlo (SMC) methods ... . Over the last few years several closely related algorithms have appeared under the names 'boostrap filters', 'particle filters', 'Monte Carlo filters', and 'survival of the fittest'. The book under review brings together many of these algorithms and presents theoretical developments ... . This book will be of great value to advanced students, researchers, and practitioners who want to learn about sequential Monte Carlo methods for the computational problems of Bayesian Statistics." (E. Novak, Metrika, May, 2003)

"This book provides a very good overview of the sequential Monte Carlo methods and contains many ideas on further research on methodologies and newer areas of application. ... It will be certainly a valuable reference book for students and researchers working in the area of on-line data analysis. ... the techniques discussed in this book are of great relevance to practitioners dealing with real time data." (Pradipta Sarkar, Technometrics, Vol. 45 (1), 2003)

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Paperback

Published: 1st December 2010

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Foreword	p. v
Acknowledgments	p. vii
Contributors	p. xxi
Introduction	p. 1
An Introduction to Sequential Monte Carlo Methods	p. 3
Motivation	p. 3
Problem statement	p. 5
Monte Carlo methods	p. 6
Perfect Monte Carlo sampling	p. 7
Importance sampling	p. 8
The Bootstrap filter	p. 10
Discussion	p. 13
Theoretical Issues	p. 15
Particle Filters - A Theoretical Perspective	p. 17
Introduction	p. 17
Notation and terminology	p. 17
Markov chains and transition kernels	p. 18
The filtering problem	p. 19
Convergence of measure-valued random variables	p. 20
Convergence theorems	p. 21
The fixed observation case	p. 21
The random observation case	p. 24
Examples of particle filters	p. 25
Description of the particle filters	p. 25
Branching mechanisms	p. 28
Convergence of the algorithm	p. 31
Discussion	p. 33
Appendix	p. 35
Conditional probabilities and conditional expectations	p. 35
The recurrence formula for the conditional distribution of the signal	p. 38
Interacting Particle Filtering With Discrete Observations	p. 43
Introduction	p. 43
Nonlinear filtering: general facts	p. 46
An interacting particle system under Case A	p. 48
Subcase A1	p. 48
Subcase A2	p. 55
An interacting particle system under Case B	p. 60
Subcase B1	p. 60
Subcase B2	p. 67
Discretely observed stochastic differential equations	p. 71
Case A	p. 72
Case B	p. 73
Strategies for Improving Sequential Monte Carlo Methods	p. 77
Sequential Monte Carlo Methods for Optimal Filtering	p. 79
Introduction	p. 79
Bayesian filtering and sequential estimation	p. 79
Dynamic modelling and Bayesian filtering	p. 79
Alternative dynamic models	p. 80
Sequential Monte Carlo Methods	p. 82
Methodology	p. 82
A generic algorithm	p. 85
Convergence results	p. 86
Application to digital communications	p. 88
Model specification and estimation objectives	p. 89
SMC applied to demodulation	p. 91
Simulations	p. 93
Deterministic and Stochastic Particle Filters in State-Space Models	p. 97
Introduction	p. 97
General issues	p. 98
Model and exact filter	p. 98
Particle filters	p. 99
Gaussian quadrature	p. 100
Quadrature filters	p. 101
Numerical error	p. 102
A small illustrative example	p. 104
Case studies from ecology	p. 104
Problem area and models	p. 104
Quadrature filters in practice	p. 107
Numerical experiments	p. 110
Concluding remarks	p. 112
Appendix: Derivation of numerical errors	p. 114
RESAMPLE-MOVE Filtering with Cross-Model Jumps	p. 117
Introduction	p. 117
Problem statement	p. 118
The RESAMPLE-MOVE algorithm	p. 119
Comments	p. 124
Central limit theorem	p. 125
Dealing with model uncertainty	p. 126
Illustrative application	p. 129
Applying RESAMPLE-MOVE	p. 131
Simulation experiment	p. 134
Uncertainty about the type of target	p. 135
Conclusions	p. 138
Improvement Strategies for Monte Carlo Particle Filters	p. 139
Introduction	p. 139
General sequential importance sampling	p. 140
Markov chain moves	p. 143
The use of bridging densities with MCMC moves	p. 144
Simulation example: TVAR model in noise	p. 145
Particle filter algorithms for TVAR models	p. 146
Bootstrap (SIR) filter	p. 148
Auxiliary particle filter (APF)	p. 149
MCMC resampling	p. 150
Simulation results	p. 152
Summary	p. 157
Acknowledgements	p. 158
Approximating and Maximising the Likelihood for a General State-Space Model	p. 159
Introduction	p. 159
Bayesian methods	p. 159
Pointwise Monte Carlo approximation of the likelihood	p. 161
Examples	p. 161
Approximation of the likelihood function based on filter samples	p. 164
Approximations based on smoother samples	p. 166
Approximation of the likelihood function	p. 167
Stochastic EM-algorithm	p. 167
Comparison of the methods	p. 168
AR(1) process	p. 168
Nonlinear example, 3 parameters	p. 171
Nonlinear model, 5 parameters	p. 173
Discussion	p. 173
Recursive estimation	p. 173
Monte Carlo Smoothing and Self-Organising State-Space Model	p. 177
Introduction	p. 177
General state-space model and state estimation	p. 178
The model and the state estimation problem	p. 178
Non-Gaussian filter and smoother	p. 179
Monte Carlo filter and smoother	p. 180
Approximation of non-Gaussian distributions	p. 180
Monte Carlo filtering	p. 181
Derivation of the Monte Carlo filter	p. 182
Monte Carlo smoothing	p. 183
Non-Gaussian smoothing for the stochastic volatility model	p. 186
Nonlinear Smoothing	p. 188
Self-organising state-space models	p. 189
Likelihood of the model and parameter estimation	p. 189
Self-organising state-space model	p. 191
Examples	p. 192
Self-organising smoothing for the stochastic volatility model	p. 192
Time series with trend and stochastic volatility	p. 194
Conclusion	p. 195
Combined Parameter and State Estimation in Simulation-Based Filtering	p. 197
Introduction and historical perspective	p. 197
General framework	p. 199
Dynamic model and analysis perspective	p. 199
Filtering for states	p. 200
Filtering for states and parameters	p. 202
The treatment of model parameters	p. 202
Artificial evolution of parameters	p. 202
Kernel smoothing of parameters	p. 203
Reinterpreting artificial parameter evolutions	p. 204
A general algorithm	p. 206
Factor stochastic volatility modelling	p. 208
Discussion and future directions	p. 217
A Theoretical Framework for Sequential Importance Sampling with Resampling	p. 225
Introduction	p. 225
Sequential importance sampling principle	p. 227
Properly weighted sample	p. 227
Sequential build-up	p. 228
Operations for enhancing SIS	p. 229
Reweighting, resampling and reallocation	p. 230
Rejection control and partial rejection control	p. 231
Marginalisation	p. 234
Monte Carlo filter for state-space models	p. 234
The general state-space model	p. 235
Conditional dynamic linear model and the mixture Kalman filter	p. 236
Some examples	p. 237
A simple illustration	p. 237
Target tracking with MKF	p. 239
Discussion	p. 241
Acknowledgements	p. 242
Improving Regularised Particle Filters	p. 247
Introduction	p. 247
Particle filters	p. 249
The (classical) interacting particle filter (IPF)	p. 250
Regularised particle filters (RPF)	p. 251
Progressive correction	p. 255
Focus on the correction step	p. 256
Principle of progressive correction	p. 257
Adaptive choice of the decomposition	p. 258
The local rejection regularised particle filter (L2RPF)	p. 260
Description of the filter	p. 260
Computing the coefficient c[superscript (i) subscript t]([alpha subscript t])	p. 263
Applications to tracking problems	p. 264
Range and bearing	p. 265
Bearings-only	p. 266
Multiple model particle filter (MMPF)	p. 269
Auxiliary Variable Based Particle Filters	p. 273
Introduction	p. 273
Particle filters	p. 274
The definition of particle filters	p. 274
Sampling the empirical prediction density	p. 274
Weaknesses of particle filters	p. 276
Auxiliary variable	p. 277
The basics	p. 277
A generic SIR based auxiliary proposal	p. 278
Examples of adaption	p. 283
Fixed-lag filtering	p. 288
Reduced random sampling	p. 289
Basic ideas	p. 289
Simple outlier example	p. 290
Conclusion	p. 292
Acknowledgements	p. 293
Improved Particle Filters and Smoothing	p. 295
Introduction	p. 295
The methods	p. 296
The smooth bootstrap	p. 296
Adaptive importance sampling	p. 300
The kernel sampler of Hurzeler and Kunsch	p. 302
Partially smooth bootstrap	p. 303
Roughening and sample augmentation	p. 305
Application of the methods in particle filtering and smoothing	p. 306
Application of smooth bootstrap procedures to a simple control problem	p. 308
Description of the problem	p. 308
An approach to the continuous-time version of the problem	p. 309
An adaptation of Titterington's method	p. 310
Probabilistic criterion 1	p. 310
Probabilistic criterion 2: working directly with the cost	p. 311
Unknown variances	p. 311
Resampling implementation	p. 312
Simulation results	p. 314
Further work on this problem	p. 317
Applications	p. 319
Posterior Cramer-Rao Bounds for Sequential Estimation	p. 321
Introduction	p. 321
Review of the posterior Cramer-Rao bound	p. 322
Bounds for sequential estimation	p. 323
Estimation model	p. 324
Posterior Cramer-Rao bound	p. 325
Relative Monte Carlo evaluation	p. 327
Example--terrain navigation	p. 329
Conclusions	p. 338
Statistical Models of Visual Shape and Motion	p. 339
Introduction	p. 339
Statistical modelling of shape	p. 341
Statistical modelling of image observations	p. 343
Sampling methods	p. 345
Modelling dynamics	p. 346
Learning dynamics	p. 349
Particle filtering	p. 352
Dynamics with discrete states	p. 354
Conclusions	p. 355
Sequential Monte Carlo Methods for Neural Networks	p. 359
Introduction	p. 359
Model specification	p. 360
MLP models for regression and classification	p. 360
Variable dimension RBF models	p. 362
Estimation objectives	p. 365
General SMC algorithm	p. 366
Importance sampling step	p. 367
Selection step	p. 368
MCMC Step	p. 369
Exact step	p. 371
On-line classification	p. 371
Simple classification example	p. 372
An application to fault detection in marine diesel engines	p. 373
An application to financial time series	p. 375
Conclusions	p. 379
Sequential Estimation of Signals under Model Uncertainty	p. 381
Introduction	p. 381
The problem of parameter estimation under uncertainty	p. 383
Sequential updating of the solution	p. 384
Sequential algorithm for computing the solution	p. 389
A Sequential-Importance-Resampling scheme	p. 390
Sequential sampling scheme based on mixtures	p. 395
Example	p. 397
Conclusions	p. 400
Acknowledgment	p. 400
Particle Filters for Mobile Robot Localization	p. 401
Introduction	p. 401
Monte Carlo localization	p. 403
Bayes filtering	p. 403
Models of robot motion and perception	p. 404
Implementation as particle filters	p. 405
Robot results	p. 408
Comparison to grid-based localization	p. 410
MCL with mixture proposal distributions	p. 414
The need for better sampling	p. 414
An alternative proposal distribution	p. 416
The mixture proposal distribution	p. 419
Robot results	p. 420
Multi-robot MCL	p. 423
Basic considerations	p. 423
Robot results	p. 425
Conclusion	p. 426
Self-Organizing Time Series Model	p. 429
Introduction	p. 429
Generalised state-space model	p. 429
Monte Carlo filter	p. 430
Self-organizing time series model	p. 432
Genetic algorithm filter	p. 432
Self-organizing state-space model	p. 434
Resampling scheme for filtering	p. 435
Selection scheme	p. 435
Comparison of performance: simulation study	p. 436
Application	p. 438
Time-varying frequency wave in small count data	p. 438
Self-organizing state-space model for time-varying frequency wave	p. 439
Results	p. 440
Conclusions	p. 444
Sampling in Factored Dynamic Systems	p. 445
Introduction	p. 445
Structured probabilistic models	p. 448
Bayesian networks	p. 448
Hybrid networks	p. 449
Dynamic Bayesian networks	p. 451
Particle filtering for DBNs	p. 454
Experimental results	p. 457
Conclusions	p. 464
In-Situ Ellipsometry Solutions Using Sequential Monte Carlo	p. 465
Introduction	p. 465
Application background	p. 465
State-space model	p. 467
Ellipsometry measurement model	p. 468
System evolution model	p. 471
Particle filter	p. 472
Results	p. 474
Conclusion	p. 475
Acknowledgments	p. 477
Manoeuvring Target Tracking Using a Multiple-Model Bootstrap Filter	p. 479
Introduction	p. 479
Optimal multiple-model solution	p. 481
The IMM algorithm	p. 483
Multiple model bootstrap filter	p. 484
Example	p. 486
Target tracking examples	p. 488
Target scenarios	p. 488
Linear, Gaussian tests	p. 488
Polar simulation results	p. 492
Conclusions	p. 495
Acknowledgments	p. 496
Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks	p. 499
Introduction	p. 499
RBPF in general	p. 500
How do we choose which nodes to sample?	p. 503
The RBPF algorithm in detail	p. 506
Application: concurrent localisation and map learning for a mobile robot	p. 508
Results on a one-dimensional grid	p. 511
Results on a two-dimensional grid	p. 514
Conclusions and future work	p. 515
Particles and Mixtures for Tracking and Guidance	p. 517
Introduction	p. 517
Guidance as a stochastic control problem	p. 518
Information state	p. 519
Dynamic programming and the dual effect	p. 520
Separability and certainty equivalence	p. 521
Sub-optimal strategies	p. 522
Derivation of control laws from particles	p. 523
Certainty equivalence control	p. 523
A scheme based on open-loop feedback control	p. 524
Guidance in the presence of intermittent spurious objects and clutter	p. 525
Introduction	p. 525
Problem formulation	p. 525
Simulation example	p. 526
Guidance results	p. 528
Monte Carlo Techniques for Automated Target Recognition	p. 533
Introduction	p. 533
The Bayesian posterior	p. 535
Inference engines	p. 536
Jump-diffusion sampling	p. 539
Diffusion Processes	p. 540
Jump processes	p. 541
Jump-diffusion algorithm	p. 544
Sensor models	p. 545
Experiments	p. 547
Acknowledgments	p. 552
Bibliography	p. 553
Index	p. 577
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Sequential Monte Carlo Methods in Practice

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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Paperback

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