Advanced Markov chain Monte Carlo methods: learning from past samples
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester
Wiley
2010
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Wiley series in computational statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIX, 357 S. graph. Darst. |
| ISBN: | 9780470748268 |
Internformat
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| 245 | 1 | 0 | |a Advanced Markov chain Monte Carlo methods |b learning from past samples |c Faming Liang ; Chuanhai Liu ; Raymond J. Carroll |
| 250 | |a 1. publ. | ||
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| 300 | |a XIX, 357 S. |b graph. Darst. | ||
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| 490 | 0 | |a Wiley series in computational statistics | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Monte Carlo method | |
| 650 | 4 | |a Markov processes | |
| 700 | 1 | |a Liu, Chuanhai |d 1959- |e Sonstige |0 (DE-588)142196568 |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804143199196807168 |
|---|---|
| adam_text | Titel: Advanced Markov chain Monte Carlo methods
Autor: Liang, Faming
Jahr: 2010
Contents
Preface xiii
Acknowledgments xvii
Publisher s Acknowledgments xix
Bayesian Inference and Markov Chain Monte Carlo 1
1.1 Bayes ................................ 1
1.1.1 Specification of Bayesian Models............. 2
1.1.2 The Jeffreys Priors and Beyond.............. 2
1.2 Bayes Output............................ 4
1.2.1 Credible Intervals and Regions.............. 4
1.2.2 Hypothesis Testing: Bayes Factors............ 5
1.3 Monte Carlo Integration...................... 8
1.3.1 The Problem........................ 8
1.3.2 Monte Carlo Approximation................ 9
1.3.3 Monte Carlo via Importance Sampling.......... 9
1.4 Random Variable Generation................... 10
1.4.1 Direct or Transformation Methods............ 11
1.4.2 Acceptance-Rejection Methods.............. 11
1.4.3 The Ratio-of-Uniforms Method and Beyond....... 14
1.4.4 Adaptive Rejection Sampling............... 18
1.4.5 Perfect Sampling...................... 18
1.5 Markov Chain Monte Carlo.................... 18
1.5.1 Markov Chains....................... 18
1.5.2 Convergence Results.................... 20
1.5.3 Convergence Diagnostics.................. 23
Exercises .............................. 24
The Gibbs Sampler 27
2.1 The Gibbs Sampler......................... 27
2.2 Data Augmentation ........................ 30
viii CONTENTS
2.3 Implementation Strategies and Acceleration Methods...... 33
2.3.1 Blocking and Collapsing.................. 33
2.3.2 Hierarchical Centering and Reparameterization..... 34
2.3.3 Parameter Expansion for Data Augmentation...... 35
2.3.4 Alternating Subspace-Spanning Resampling....... 43
2.4 Applications............................. 45
2.4.1 The Student-t Model.................... 45
2.4.2 Robit Regression or Binary Regression with
the Student-t Link..................... 47
2.4.3 Linear Regression with Interval-Censored Responses . . 50
Exercises .............................. 54
Appendix 2A: The EM and PX-EM Algorithms......... 56
3 The Metropolis-Hastings Algorithm 59
3.1 The Metropolis-Hastings Algorithm................ 59
3.1.1 Independence Sampler................... 62
3.1.2 Random Walk Chains................... 63
3.1.3 Problems with Metropolis-Hastings Simulations..... 63
3.2 Variants of the Metropolis-Hastings Algorithm......... 65
3.2.1 The Hit-and-Run Algorithm................ 65
3.2.2 The Langevin Algorithm.................. 65
3.2.3 The Multiple-Try MH Algorithm............. 66
3.3 Reversible Jump MCMC Algorithm for Bayesian Model Selec-
tion Problems............................ 67
3.3.1 Reversible Jump MCMC Algorithm........... 67
3.3.2 Change-Point Identification................ 70
3.4 Metropolis-Within-Gibbs Sampler for ChlP-chip Data Analysis 75
3.4.1 Metropolis-Within-Gibbs Sampler............ 75
3.4.2 Bayesian Analysis for ChlP-chip Data.......... 76
Exercises .............................. 83
4 Auxiliary Variable MCMC Methods 85
4.1 Simulated Annealing........................ 86
4.2 Simulated Tempering........................ 88
4.3 The Slice Sampler ......................... 90
4.4 The Swendsen-Wang Algorithm.................. 91
4.5 The Wolff Algorithm........................ 93
4.6 The M0ller Algorithm....................... 95
4.7 The Exchange Algorithm ..................... 97
4.8 The Double MH Sampler ..................... 98
4.8.1 Spatial Autologistic Models................ 99
4.9 Monte Carlo MH Sampler..................... 103
4.9.1 Monte Carlo MH Algorithm................ 103
4.9.2 Convergence ........................ 107
CONTENTS ix
4.9.3 Spatial Autologistic Models (Revisited) .........110
4.9.4 Marginal Inference.....................Ill
4.10 Applications.............................113
4.10.1 Autonormal Models....................114
4.10.2 Social Networks.......................116
Exercises ..............................121
5 Population-Based MCMC Methods 123
5.1 Adaptive Direction Sampling...................124
5.2 Conjugate Gradient Monte Carlo.................125
5.3 Sample Metropolis-Hastings Algorithm..............126
5.4 Parallel Tempering.........................127
5.5 Evolutionary Monte Carlo.....................128
5.5.1 Evolutionary Monte Carlo in Binary-Coded Space . . . 129
5.5.2 Evolutionary Monte Carlo in Continuous Space.....132
5.5.3 Implementation Issues...................133
5.5.4 Two Illustrative Examples.................134
5.5.5 Discussion..........................139
5.6 Sequential Parallel Tempering for Simulation of High Dimen-
sional Systems ...........................140
5.6.1 Build-up Ladder Construction ..............141
5.6.2 Sequential Parallel Tempering...............142
5.6.3 An Illustrative Example: the Witch s Hat Distribution . 142
5.6.4 Discussion..........................145
5.7 Equi-Energy Sampler........................146
5.8 Applications.............................148
5.8.1 Bayesian Curve Fitting ..................148
5.8.2 Protein Folding Simulations: 2D HP Model.......153
5.8.3 Bayesian Neural Networks for Nonlinear Time Series
Forecasting.........................156
Exercises ..............................162
Appendix 5A: Protein Sequences for 2D HP Models ......163
6 Dynamic Weighting 165
6.1 Dynamic Weighting ........................165
6.1.1 The IWIW Principle....................165
6.1.2 Tempering Dynamic Weighting Algorithm........167
6.1.3 Dynamic Weighting in Optimization...........171
6.2 Dynamically Weighted Importance Sampling..........173
6.2.1 The Basic Idea.......................173
6.2.2 A Theory of DWIS ....................174
6.2.3 Some IWIWp Transition Rules..............176
6.2.4 Two DWIS Schemes....................179
6.2.5 Weight Behavior Analysis.................180
CONTENTS
6.2.6 A Numerical Example...................183
6.3 Monte Carlo Dynamically Weighted Importance Sampling . . . 185
6.3.1 Sampling from Distributions with Intractable
Normalizing Constants...................185
6.3.2 Monte Carlo Dynamically Weighted Importance
Sampling..........................186
6.3.3 Bayesian Analysis for Spatial Autologistic Models . . . 191
6.4 Sequentially Dynamically Weighted Importance Sampling . . . 195
Exercises ..............................197
Stochastic Approximation Monte Carlo 199
7.1 Multicanonical Monte Carlo....................200
7.2 1/fc-Ensemble Sampling......................202
7.3 The Wang-Landau Algorithm...................204
7.4 Stochastic Approximation Monte Carlo .............207
7.5 Applications of Stochastic Approximation Monte Carlo.....218
7.5.1 Efficient p-Value Evaluation for Resampling-
Based Tests.........................218
7.5.2 Bayesian Phylogeny Inference...............222
7.5.3 Bayesian Network Learning................227
7.6 Variants of Stochastic Approximation Monte Carlo.......233
7.6.1 Smoothing SAMC for Model Selection Problems .... 233
7.6.2 Continuous SAMC for Marginal Density Estimation . . 239
7.6.3 Annealing SAMC for Global Optimization........244
7.7 Theory of Stochastic Approximation Monte Carlo........253
7.7.1 Convergence ........................253
7.7.2 Convergence Rate .....................267
7.7.3 Ergodicity and its IWIW Property............271
7.8 Trajectory Averaging: Toward the Optimal
Convergence Rate .........................275
7.8.1 Trajectory Averaging for a SAMCMC Algorithm .... 277
7.8.2 Trajectory Averaging for SAMC .............279
7.8.3 Proof of Theorems 7.8.2 and 7.8.3.............281
Exercises ..............................296
Appendix 7A: Test Functions for Global Optimization.....298
Markov Chain Monte Carlo with Adaptive Proposals 305
8.1 Stochastic Approximation-Based Adaptive Algorithms.....306
8.1.1 Ergodicity and Weak Law of Large Numbers......307
8.1.2 Adaptive Metropolis Algorithms.............309
8.2 Adaptive Independent Metropolis-Hastings Algorithms.....312
8.3 Regeneration-Based Adaptive Algorithms............315
8.3.1 Identification of Regeneration Times...........315
8.3.2 Proposal Adaptation at Regeneration Times.......317
CONTENTS xi
8.4 Population-Based Adaptive Algorithms .............317
8.4.1 ADS, EMC, NKC and More................317
8.4.2 Adaptive EMC.......................318
8.4.3 Application to Sensor Placement Problems.......323
Exercises ..............................324
References 327
Index 353
|
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| discipline | Mathematik |
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| indexdate | 2024-07-09T22:43:52Z |
| institution | BVB |
| isbn | 9780470748268 |
| language | English |
| lccn | 2010013148 |
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| spelling | Liang, Faming 1970- Verfasser (DE-588)130820547 aut Advanced Markov chain Monte Carlo methods learning from past samples Faming Liang ; Chuanhai Liu ; Raymond J. Carroll 1. publ. Chichester Wiley 2010 XIX, 357 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in computational statistics Includes bibliographical references and index Monte Carlo method Markov processes Liu, Chuanhai 1959- Sonstige (DE-588)142196568 oth Carroll, Raymond J. 1949- Sonstige (DE-588)111805708 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020519250&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Liang, Faming 1970- Advanced Markov chain Monte Carlo methods learning from past samples Monte Carlo method Markov processes |
| title | Advanced Markov chain Monte Carlo methods learning from past samples |
| title_auth | Advanced Markov chain Monte Carlo methods learning from past samples |
| title_exact_search | Advanced Markov chain Monte Carlo methods learning from past samples |
| title_full | Advanced Markov chain Monte Carlo methods learning from past samples Faming Liang ; Chuanhai Liu ; Raymond J. Carroll |
| title_fullStr | Advanced Markov chain Monte Carlo methods learning from past samples Faming Liang ; Chuanhai Liu ; Raymond J. Carroll |
| title_full_unstemmed | Advanced Markov chain Monte Carlo methods learning from past samples Faming Liang ; Chuanhai Liu ; Raymond J. Carroll |
| title_short | Advanced Markov chain Monte Carlo methods |
| title_sort | advanced markov chain monte carlo methods learning from past samples |
| title_sub | learning from past samples |
| topic | Monte Carlo method Markov processes |
| topic_facet | Monte Carlo method Markov processes |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020519250&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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