Sequential Monte Carlo Methods in practice:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2001
|
| Schriftenreihe: | Statistics for engineering and information science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXVII, 581 S. Ill., graph. Darst. |
| ISBN: | 0387951466 9780387951461 9781441928870 |
Internformat
MARC
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| 245 | 1 | 0 | |a Sequential Monte Carlo Methods in practice |c Arnaud Doucet ... eds. |
| 246 | 1 | 3 | |a Sequential Monte-Carlo-Methods in practice |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2001 | |
| 300 | |a XXVII, 581 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Statistics for engineering and information science | |
| 650 | 4 | |a Monte-Carlo-Simulation | |
| 650 | 4 | |a Monte Carlo method | |
| 650 | 0 | 7 | |a Monte-Carlo-Simulation |0 (DE-588)4240945-7 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4143413-4 |a Aufsatzsammlung |2 gnd-content | |
| 689 | 0 | 0 | |a Monte-Carlo-Simulation |0 (DE-588)4240945-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Doucet, Arnaud |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4757-3437-9 |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009373553 | ||
Datensatz im Suchindex
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|---|---|
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| DE-BY-FWS_katkey | 435076 |
| DE-BY-FWS_media_number | 083101216376 |
| _version_ | 1806176381949706240 |
| adam_text | Contents
Foreword v
Acknowledgments vii
Contributors xxi
I Introduction 1
1 An Introduction to Sequential Monte Carlo Methods 3
Arnaud Doucet, Nando de Freitas, and Neil Gordon
1.1 Motivation 3
1.2 Problem statement 5
1.3 Monte Carlo methods 6
1.3.1 Perfect Monte Carlo sampling 7
1.3.2 Importance sampling 8
1.3.3 The Bootstrap filter 10
1.4 Discussion 13
II Theoretical Issues 15
2 Particle Filters A Theoretical Perspective 17
Dan Crisan
2.1 Introduction 17
2.2 Notation and terminology 17
2.2.1 Markov chains and transition kernels 18
2.2.2 The filtering problem 19
2.2.3 Convergence of measure valued random variables . 20
2.3 Convergence theorems 21
2.3.1 The fixed observation case 21
2.3.2 The random observation case 24
2.4 Examples of particle filters 25
2.4.1 Description of the particle niters 25
x Contents
2.4.2 Branching mechanisms 28
2.4.3 Convergence of the algorithm 31
2.5 Discussion 33
2.6 Appendix 35
2.6.1 Conditional probabilities and conditional
expectations 35
2.6.2 The recurrence formula for the conditional
distribution of the signal 38
3 Interacting Particle Filtering With Discrete Observations 43
Pierre Del Moral and Jean Jacod
3.1 Introduction 43
3.2 Nonlinear filtering: general facts 46
3.3 An interacting particle system under Case A 48
3.3.1 Subcase Al 48
3.3.2 Subcase A2 55
3.4 An interacting particle system under Case B 60
3.4.1 Subcase Bl 60
3.4.2 Subcase B2 67
3.5 Discretely observed stochastic differential equations .... 71
3.5.1 Case A 72
3.5.2 Case B 73
III Strategies for Improving Sequential Monte
Carlo Methods 77
4 Sequential Monte Carlo Methods for Optimal Filtering 79
Christophe Andrieu, Arnaud Doucet, and Elena Punskaya
4.1 Introduction 79
4.2 Bayesian filtering and sequential estimation 79
4.2.1 Dynamic modelling and Bayesian filtering 79
4.2.2 Alternative dynamic models 80
4.3 Sequential Monte Carlo Methods 82
4.3.1 Methodology 82
4.3.2 A generic algorithm 85
4.3.3 Convergence results 86
4.4 Application to digital communications 88
4.4.1 Model specification and estimation objectives ... 89
4.4.2 SMC applied to demodulation 91
4.4.3 Simulations 93
Contents xi
5 Deterministic and Stochastic Particle Filters in State
Space Models 97
Erik B0lviken and Geir Storvik
5.1 Introduction 97
5.2 General issues 98
5.2.1 Model and exact filter 98
5.2.2 Particle filters 99
5.2.3 Gaussian quadrature 100
5.2.4 Quadrature filters 101
5.2.5 Numerical error 102
5.2.6 A small illustrative example 104
5.3 Case studies from ecology 104
5.3.1 Problem area and models 104
5.3.2 Quadrature filters in practice 107
5.3.3 Numerical experiments 110
5.4 Concluding remarks 112
5.5 Appendix: Derivation of numerical errors 114
6 RES AMPLE MOVE Filtering with Cross Model Jumps 117
Carlo Berzuini and Walter Gilks
6.1 Introduction 117
6.2 Problem statement 118
6.3 The RES AMPLE MOVE algorithm 119
6.4 Comments 124
6.5 Central limit theorem 125
6.6 Dealing with model uncertainty 126
6.7 Illustrative application 129
6.7.1 Applying RESAMPLE MOVE 131
6.7.2 Simulation experiment 134
6.7.3 Uncertainty about the type of target 135
6.8 Conclusions 138
7 Improvement Strategies for Monte Carlo Particle Filters 139
Simon Godsill and Tim Clapp
7.1 Introduction 139
7.2 General sequential importance sampling 140
7.3 Markov chain moves 143
7.3.1 The use of bridging densities with MCMC moves . 144
7.4 Simulation example: TVAR model in noise 145
7.4.1 Particle filter algorithms for TVAR models .... 146
7.4.2 Bootstrap (SIR) filter 148
7.4.3 Auxiliary particle filter (APF) 149
7.4.4 MCMC resampling 150
7.4.5 Simulation results 152
7.5 Summary 157
xii Contents
7.6 Acknowledgements 158
8 Approximating and Maximising the Likelihood for a
General State Space Model 159
Markus Hiirzeler and Hans R. Kiinsch
8.1 Introduction 159
8.2 Bayesian methods 159
8.3 Pointwise Monte Carlo approximation of the likelihood . . 161
8.3.1 Examples 161
8.4 Approximation of the likelihood function based on filter
samples 164
8.5 Approximations based on smoother samples 166
8.5.1 Approximation of the likelihood function 167
8.5.2 Stochastic EM algorithm 167
8.6 Comparison of the methods 168
8.6.1 AR(1) process 168
8.6.2 Nonlinear example, 3 parameters 171
8.6.3 Nonlinear model, 5 parameters 173
8.6.4 Discussion 173
8.7 Recursive estimation 173
9 Monte Carlo Smoothing and Self Organising State Space
Model 177
Genshiro Kitagawa and Seisho Sato
9.1 Introduction 177
9.2 General state space model and state estimation 178
9.2.1 The model and the state estimation problem . . . 178
9.2.2 Non Gaussian filter and smoother 179
9.3 Monte Carlo filter and smoother 180
9.3.1 Approximation of non Gaussian distributions . . . 180
9.3.2 Monte Carlo filtering 181
9.3.3 Derivation of the Monte Carlo filter 182
9.3.4 Monte Carlo smoothing 183
9.3.5 Non Gaussian smoothing for the stochastic
volatility model 186
9.3.6 Nonlinear Smoothing 188
9.4 Self organising state space models 189
9.4.1 Likelihood of the model and parameter estimation . 189
9.4.2 Self organising state space model 191
9.5 Examples 192
9.5.1 Self organising smoothing for the stochastic
volatility model 192
9.5.2 Time series with trend and stochastic volatility . . 194
9.6 Conclusion 195
Contents xiii
10 Combined Parameter and State Estimation in Simulation
Based Filtering 197
Jane Liu and Mike West
10.1 Introduction and historical perspective 197
10.2 General framework 199
10.2.1 Dynamic model and analysis perspective 199
10.2.2 Filtering for states 200
10.2.3 Filtering for states and parameters 202
10.3 The treatment of model parameters 202
10.3.1 Artificial evolution of parameters 202
10.3.2 Kernel smoothing of parameters 203
10.3.3 Reinterpreting artificial parameter evolutions . . . 204
10.4 A general algorithm 206
10.5 Factor stochastic volatility modelling 208
10.6 Discussion and future directions 217
11 A Theoretical Framework for Sequential Importance
Sampling with Resampling 225
Jun S. Liu, Rong Chen, and Tanya Logvinenko
11.1 Introduction 225
11.2 Sequential importance sampling principle 227
11.2.1 Properly weighted sample 227
11.2.2 Sequential build up 228
11.3 Operations for enhancing SIS 229
11.3.1 Reweighting, resampling and reallocation 230
11.3.2 Rejection control and partial rejection control . . . 231
11.3.3 Marginalisation 234
11.4 Monte Carlo filter for state space models 234
11.4.1 The general state space model 235
11.4.2 Conditional dynamic linear model and the
mixture Kalman filter 236
11.5 Some examples 237
11.5.1 A simple illustration 237
11.5.2 Target tracking with MKF 239
11.6 Discussion 241
11.7 Acknowledgements 242
12 Improving Regularised Particle Filters 247
Christian Musso, Nadia Oudjane, and Francois Le Gland
12.1 Introduction 247
12.2 Particle filters 249
12.2.1 The (classical) interacting particle filter (IPF) ... 250
12.2.2 Regularised particle filters (RPF) 251
12.3 Progressive correction 255
12.3.1 Focus on the correction step 256
xiv Contents
12.3.2 Principle of progressive correction 257
12.3.3 Adaptive choice of the decomposition 258
12.4 The local rejection regularised particle filter (L2RPF) . . 260
12.4.1 Description of the filter 260
12.4.2 Computing the coefficient c^ at) 263
12.5 Applications to tracking problems 264
12.5.1 Range and bearing 265
12.5.2 Bearings only 266
12.5.3 Multiple model particle filter (MMPF) 269
13 Auxiliary Variable Based Particle Filters 273
Michael K. Pitt and Neil Shephard
13.1 Introduction 273
13.2 Particle niters 274
13.2.1 The definition of particle niters 274
13.2.2 Sampling the empirical prediction density 274
13.2.3 Weaknesses of particle filters 276
13.3 Auxiliary variable 277
13.3.1 The basics 277
13.3.2 A generic SIR based auxiliary proposal 278
13.3.3 Examples of adaption 283
13.4 Fixed lag filtering 288
13.5 Reduced random sampling 289
13.5.1 Basic ideas 289
13.5.2 Simple outlier example 290
13.6 Conclusion 292
13.7 Acknowledgements 293
14 Improved Particle Filters and Smoothing 295
Photis Stavropoulos and D.M. Titterington
14.1 Introduction 295
14.2 The methods 296
14.2.1 The smooth bootstrap 296
14.2.2 Adaptive importance sampling 300
14.2.3 The kernel sampler of Hiirzeler and Kiinsch .... 302
14.2.4 Partially smooth bootstrap 303
14.2.5 Roughening and sample augmentation 305
14.2.6 Application of the methods in particle filtering
and smoothing 306
14.3 Application of smooth bootstrap procedures to a simple
control problem 308
14.3.1 Description of the problem 308
14.3.2 An approach to the continuous time version of
the problem 309
14.3.3 An adaptation of Titterington s method 310
Contents xv
14.3.4 Probabilistic criterion 1 310
14.3.5 Probabilistic criterion 2: working directly with
the cost 311
14.3.6 Unknown variances 311
14.3.7 Resampling implementation 312
14.3.8 Simulation results 314
14.3.9 Further work on this problem 317
IV Applications 319
15 Posterior Cramer Rao Bounds for Sequential Estimation 321
Niclas Bergman
15.1 Introduction 321
15.2 Review of the posterior Cramer Rao bound 322
15.3 Bounds for sequential estimation 323
15.3.1 Estimation model 324
15.3.2 Posterior Cramer Rao bound 325
15.3.3 Relative Monte Carlo evaluation 327
15.4 Example terrain navigation 329
15.5 Conclusions 338
16 Statistical Models of Visual Shape and Motion 339
Andrew Blake, Michael Isard, and John MacCormick
16.1 Introduction 339
16.2 Statistical modelling of shape 341
16.3 Statistical modelling of image observations 343
16.4 Sampling methods 345
16.5 Modelling dynamics 346
16.6 Learning dynamics 349
16.7 Particle filtering 352
16.8 Dynamics with discrete states 354
16.9 Conclusions 355
17 Sequential Monte Carlo Methods for Neural Networks 359
N de Freitas, C Andrieu, P H0jen S 3rensen, M Niranjan, and
A Gee
17.1 Introduction 359
17.2 Model specification 360
17.2.1 MLP models for regression and classification . . . 360
17.2.2 Variable dimension RBF models 362
17.3 Estimation objectives 365
17.4 General SMC algorithm 366
17.4.1 Importance sampling step 367
17.4.2 Selection step 368
xvi Contents
17.4.3 MCMC Step 369
17.4.4 Exact step 371
17.5 On line classification 371
17.5.1 Simple classification example 372
17.5.2 An application to fault detection in marine diesel
engines 373
17.6 An application to financial time series 375
17.7 Conclusions 379
18 Sequential Estimation of Signals under Model
Uncertainty 381
Petar M. Djuric
18.1 Introduction 381
18.2 The problem of parameter estimation under uncertainty . 383
18.3 Sequential updating of the solution 384
18.4 Sequential algorithm for computing the solution 389
18.4.1 A Sequential Importance Resampling scheme . . . 390
18.4.2 Sequential sampling scheme based on mixtures . . 395
18.5 Example 397
18.6 Conclusions 400
18.7 Acknowledgment 400
19 Particle Filters for Mobile Robot Localization 401
Dieter Fox, Sebastian Thrun, Wolfram Burgard, and Frank
Dellaert
19.1 Introduction 401
19.2 Monte Carlo localization 403
19.2.1 Bayes filtering 403
19.2.2 Models of robot motion and perception 404
19.2.3 Implementation as particle filters 405
19.2.4 Robot results 408
19.2.5 Comparison to grid based localization 410
19.3 MCL with mixture proposal distributions 414
19.3.1 The need for better sampling 414
19.3.2 An alternative proposal distribution 416
19.3.3 The mixture proposal distribution 419
19.3.4 Robot results 420
19.4 Multi robot MCL 423
19.4.1 Basic considerations 423
19.4.2 Robot results 425
19.5 Conclusion 426
20 Self Organizing Time Series Model 429
Tomoyuki Higuchi
20.1 Introduction 429
Contents xvii
20.1.1 Generalised state space model 429
20.1.2 Monte Carlo filter 430
20.2 Self organizing time series model 432
20.2.1 Genetic algorithm filter 432
20.2.2 Self organizing state space model 434
20.3 Resampling scheme for filtering 435
20.3.1 Selection scheme 435
20.3.2 Comparison of performance: simulation study . . . 436
20.4 Application 438
20.4.1 Time varying frequency wave in small count data . 438
20.4.2 Self organizing state space model for time varying
frequency wave 439
20.4.3 Results 440
20.5 Conclusions 444
21 Sampling in Factored Dynamic Systems 445
Daphne Koller and Uri Lerner
21.1 Introduction 445
21.2 Structured probabilistic models 448
21.2.1 Bayesian networks 448
21.2.2 Hybrid networks 449
21.2.3 Dynamic Bayesian networks 451
21.3 Particle filtering for DBNs 454
21.4 Experimental results 457
21.5 Conclusions 464
22 In Situ Ellipsometry Solutions Using Sequential Monte
Carlo 465
Alan D. Marrs
22.1 Introduction 465
22.2 Application background 465
22.3 State space model 467
22.3.1 Ellipsometry measurement model 468
22.3.2 System evolution model 471
22.3.3 Particle filter 472
22.4 Results 474
22.5 Conclusion 475
22.6 Acknowledgments 477
23 Manoeuvring Target Tracking Using a Multiple Model
Bootstrap Filter 479
Shaun McGinnity and George W. Irwin
23.1 Introduction 479
23.2 Optimal multiple model solution 481
23.3 The IMM algorithm 483
xviii Contents
23.4 Multiple model bootstrap filter 484
23.4.1 Example 486
23.5 Target tracking examples 488
23.5.1 Target scenarios 488
23.5.2 Linear, Gaussian tests 488
23.5.3 Polar simulation results 492
23.6 Conclusions 495
23.7 Acknowledgments 496
24 Rao Blackwellised Particle Filtering for Dynamic Bayesian
Networks 499
Kevin Murphy and Stuart Russell
24.1 Introduction 499
24.2 RBPF in general 500
24.2.1 How do we choose which nodes to sample? 503
24.3 The RBPF algorithm in detail 506
24.4 Application: concurrent localisation and map learning
for a mobile robot 508
24.4.1 Results on a one dimensional grid 511
24.4.2 Results on a two dimensional grid 514
24.5 Conclusions and future work 515
25 Particles and Mixtures for Tracking and Guidance 517
David S almond and Neil Gordon
25.1 Introduction 517
25.1.1 Guidance as a stochastic control problem 518
25.1.2 Information state 519
25.1.3 Dynamic programming and the dual effect 520
25.1.4 Separability and certainty equivalence 521
25.1.5 Sub optimal strategies 522
25.2 Derivation of control laws from particles 523
25.2.1 Certainty equivalence control 523
25.2.2 A scheme based on open loop feedback control . . 524
25.3 Guidance in the presence of intermittent spurious objects
and clutter 525
25.3.1 Introduction 525
25.3.2 Problem formulation 525
25.3.3 Simulation example 526
25.3.4 Guidance results 528
26 Monte Carlo Techniques for Automated Target Recogni¬
tion 533
Anuj Srivastava, Aaron D. Lanterman, Ulf Grenander, Marc
Loizeaux, and Michael I. Miller
26.1 Introduction 533
Contents xix
26.1.1 The Bayesian posterior 535
26.1.2 Inference engines 536
26.2 Jump diffusion sampling 539
26.2.1 Diffusion Processes 540
26.2.2 Jump processes 541
26.2.3 Jump diffusion algorithm 544
26.3 Sensor models 545
26.4 Experiments 547
26.5 Acknowledgments 552
Bibliography 553
Index 577
|
| any_adam_object | 1 |
| building | Verbundindex |
| bvnumber | BV013717032 |
| callnumber-first | Q - Science |
| callnumber-label | QA298 |
| callnumber-raw | QA298.S47 2001 |
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| dewey-search | 519.2/82 21 519.282 |
| dewey-sort | 3519.2 282 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| genre | (DE-588)4143413-4 Aufsatzsammlung gnd-content |
| genre_facet | Aufsatzsammlung |
| id | DE-604.BV013717032 |
| illustrated | Illustrated |
| indexdate | 2024-08-01T11:20:25Z |
| institution | BVB |
| isbn | 0387951466 9780387951461 9781441928870 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009373553 |
| oclc_num | 247970465 |
| open_access_boolean | |
| owner | DE-29T DE-19 DE-BY-UBM DE-739 DE-703 DE-91G DE-BY-TUM DE-706 DE-521 DE-83 DE-11 DE-355 DE-BY-UBR DE-91 DE-BY-TUM DE-188 DE-863 DE-BY-FWS DE-20 |
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| physical | XXVII, 581 S. Ill., graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series2 | Statistics for engineering and information science |
| spellingShingle | Sequential Monte Carlo Methods in practice Monte-Carlo-Simulation Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| subject_GND | (DE-588)4240945-7 (DE-588)4143413-4 |
| title | Sequential Monte Carlo Methods in practice |
| title_alt | Sequential Monte-Carlo-Methods in practice |
| title_auth | Sequential Monte Carlo Methods in practice |
| title_exact_search | Sequential Monte Carlo Methods in practice |
| title_full | Sequential Monte Carlo Methods in practice Arnaud Doucet ... eds. |
| title_fullStr | Sequential Monte Carlo Methods in practice Arnaud Doucet ... eds. |
| title_full_unstemmed | Sequential Monte Carlo Methods in practice Arnaud Doucet ... eds. |
| title_short | Sequential Monte Carlo Methods in practice |
| title_sort | sequential monte carlo methods in practice |
| topic | Monte-Carlo-Simulation Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| topic_facet | Monte-Carlo-Simulation Monte Carlo method Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009373553&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT doucetarnaud sequentialmontecarlomethodsinpractice |
Inhaltsverzeichnis
THWS Würzburg Zentralbibliothek Lesesaal
| Signatur: |
1000 SK 820 D728st |
|---|---|
| Exemplar 1 | ausleihbar Verfügbar Bestellen |