Simulation and the Monte Carlo method:
Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years ago. Wh...
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| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, N.J.
Wiley
2008
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences." "Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method. |
| Beschreibung: | Includes index. |
| Beschreibung: | XVII, 345 S. |
| ISBN: | 9780470177945 |
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| 245 | 1 | 0 | |a Simulation and the Monte Carlo method |c Reuven Y. Rubinstein ; Dirk P. Kroese |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Hoboken, N.J. |b Wiley |c 2008 | |
| 300 | |a XVII, 345 S. | ||
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| 500 | |a Includes index. | ||
| 520 | 3 | |a Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences." "Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method. | |
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Datensatz im Suchindex
| _version_ | 1804137379420700672 |
|---|---|
| adam_text | CONTENTS
Preface
Acknowledgments
1
Preliminaries
l.l
Random Experiments
1.2
Conditional Probability and Independence
1.3
Random Variables and Probability Distributions
1.4
Some Important Distributions
1.5
Expectation
1.6
Joint Distributions
1.7
Functions of Random Variables
1.7.1
Linear Transformations
1.7.2
General Transformations
1.8
Transforms
1.9
Jointly Nonnal Random Variables
1.10
Limit Theorems
1.11
Poisson
Processes
1.12
Markov Processes
1.12.1
Markov Chains
1.12.2
Classification of States
1.12.3
Limiting Behavior
ХШ
xvii
1
2
3
5
6
7
10
11
12
13
14
15
16
18
19
20
21
vii
Viii
CONTENTS
1.12.4
Reversibility
23
1.12.5
Markov Jump Processes
24
1.13
Efficiency of Estimators 26
1.13.1
Complexity 28
1.14
Information 28
1.14.1
Shannon Entropy 29
1.14.2
Kuliback-Leibler Cross-Entropy
31
1.14.3
The Maximum Likelihood Estimator and the Score Function
32
1.14.4
Fisher Information
33
1.15
Convex Optimization and Duality
34
1.15.1
Lagrangian Method
3 6
1.15.2
Duality
37
Problems
41
References
46
2
Random Number, Random Variable, and Stochastic Process
Generation
49
2.1
Introduction
49
2.2
Random Number Generation
49
2.3
Random Variable Generation
51
2.3.1
Inverse-Transform Method
51
2.3.2
Alias Method
54
2.3.3
Composition Method
54
2.3.4
Acceptance-Rejection Method
55
2.4
Generating From Commonly Used Distributions
58
2.4.1
Generating Continuous Random Variables
58
2.4.2
Generating Discrete Random Variables
63
2.5
Random Vector Generation
65
2.5.1
Vector Acceptance-Rejection Method
66
2.5.2
Generating Variables from
a
Multinormal
Distribution
67
2.5.3
Generating Uniform Random Vectors Over a Simplex
68
2.5.4
Generating Random Vectors Uniformly Distributed Over a Unit
Hyperball and Hypersphere
69
2.5.5
Generating Random Vectors Uniformly Distributed Over a
Hyperellipsoid
70
2.6
Generating
Poisson
Processes
70
2.7
Generating Markov Chains and Markov Jump Processes
72
2.7.1
Random Walk on a Graph
72
2.7.2
Generating Markov Jump Processes
73
2.8
Generating Random Permutations
74
Problems
75
References
80
CONTENTS
ЇХ
3 Simulation
of Discrete-Event Systems
81
3.1
Simulation Models
82
3.1.1
Classification of Simulation Models
84
3.2
Simulation Clock and Event List for DEDS
85
3.3
Discrete-Event Simulation
87
3.3.1
Tandem Queue
87
3.3.2
Repairman Problem
91
Problems
94
References
96
4
Statistical Analysis of Discrete-Event Systems
97
4.1
Introduction
97
4.2
Static Simulation Models
98
4.2.1
Confidence Interval
100
4.3
Dynamic Simulation Models
101
4.3.1
Finite-Horizon Simulation
102
4.3.2
Steady-State Simulation
103
4.4
The Bootstrap Method
113
Problems
115
References
118
5
Controlling the Variance
119
5.1
Introduction
119
5.2
Common and Antithetic Random Variables
120
5.3
Control Variables
123
5.4
Conditional Monte Carlo
125
5.4.1
Variance Reduction for Reliability Models
126
5.5
Stratified Sampling
129
5.6
Importance Sampling
131
5.6.1
Weighted Samples
132
5.6.2
The Variance Minimization Method
132
5.6.3
The Cross-Entropy Method
136
5.7
Sequential Importance Sampling
141
5.7.1
Nonlinear Filtering for Hidden Markov Models
144
5.8
The Transform Likelihood Ratio Method
148
5.9
Preventing the Degeneracy of Importance Sampling
і
51
5.9.1
The Two-Stage Screening Algorithm
153
5.9.2
CaseStudy
158
Problems
161
References
165
6.1
Introduction
6.2
The Metropolis-Hastings Algorithm
6.3
The Hit-and-Run Sampler
6.4
The Gibbs Sampler
6.5
Ising and Potts Models
6.5.1
Ising Model
6.5.2
Potts Model
6.6
Bayesian Statistics
6.7
*
Other Markov Samplers
6.7.1
Slice Sampler
6.7.2
Reversible Jump Sampler
6.8
Simulated Annealing
6.9
Perfect Sampling
Problems
References
X
CONTENTS
6
Markov Chain
Monte Cario 167
167
168
173
175
178
178
179
181
183
185
186
189
192
194
199
Sensitivity Analysis and Monte Carlo Optimization
201
7.1
Introduction
201
7.2
The Score Function Method for Sensitivity Analysis of
DESS
203
7.3
Simulation-Based Optimization of
DESS
211
7.3.1
Stochastic Approximation
212
7.3.2
The Stochastic Counterpart Method
215
7.4
Sensitivity Analysis of DEDS
225
Problems
230
References
233
The Cross-Entropy Method
235
8.1
Introduction
235
8.2
Estimation of Rare-Event Probabilities
236
8.2.1
The Root-Finding Problem
245
8.2.2
The Screening Method for Rare Events
245
8.3
The
CE
Method for Optimization
249
8.4
The Max-cut Problem
253
8.5
The Partition Problem
259
8.5.1
Empirical Computational Complexity
260
8.6
The Traveling Salesman Problem
260
8.6.1
Incomplete Graphs
265
8.6.2
Node Placement
266
8.6.3
CaseStudies
267
8.7
Continuous Optimization
268
CONTENTS
XI
8.8
Noisy Optimization
269
Problems
271
References
275
9
Counting via Monte Carlo
279
9.1
Counting Problems
279
9.2
Satisfiability Problem
280
9.2.1
Random
АГ
-SAT
(AT-RSAT)
283
9.3
The Rare-Event Framework for Counting
284
9.3.1
Rare Events for the Satisfiability Problem
287
9.4
Other Randomized Algorithms for Counting
288
9.4.1
ЭС*
is a Union of Some Sets
291
9.4.2
Complexity of Randomized Algorithms: FPRAS and FPAUS
294
9.4.3
FPRAS for SATs in CNF
297
9.5
MinxEnt and Parametric MinxEnt
297
9.5.1
The MinxEnt Method
297
9.5.2
Rare-Event Probability Estimation Using
PME
301
9.6
PME
for Combinatorial Optimization Problems and Decision Making
306
9.7
Numerical Results
307
Problems
311
References
312
Appendix
315
A.
1
Cholesky Square Root Method
315
A.2 Exact Sampling from a Conditional Bernoulli Distribution
316
A.3 Exponential Families
317
A.4 Sensitivity Analysis
320
A.4.1 Convexity Results
321
A.4.2
Monotonicity
Results
322
A.5 A Simple
CE
Algorithm for Optimizing the Peaks Function
323
A.6 Discrete-time
Kalman
Filter
323
A.7 Bernoulli Disruption Problem
324
A.8 Complexity of Stochastic Programming Problems
326
Problems
334
References
335
Abbreviations and Acronyms
336
List of Symbols
338
Index
341
|
| adam_txt |
CONTENTS
Preface
Acknowledgments
1
Preliminaries
l.l
Random Experiments
1.2
Conditional Probability and Independence
1.3
Random Variables and Probability Distributions
1.4
Some Important Distributions
1.5
Expectation
1.6
Joint Distributions
1.7
Functions of Random Variables
1.7.1
Linear Transformations
1.7.2
General Transformations
1.8
Transforms
1.9
Jointly Nonnal Random Variables
1.10
Limit Theorems
1.11
Poisson
Processes
1.12
Markov Processes
1.12.1
Markov Chains
1.12.2
Classification of States
1.12.3
Limiting Behavior
ХШ
xvii
1
2
3
5
6
7
10
11
12
13
14
15
16
18
19
20
21
vii
Viii
CONTENTS
1.12.4
Reversibility
23
1.12.5
Markov Jump Processes
24
1.13
Efficiency of Estimators 26
1.13.1
Complexity 28
1.14
Information 28
1.14.1
Shannon Entropy 29
1.14.2
Kuliback-Leibler Cross-Entropy
31
1.14.3
The Maximum Likelihood Estimator and the Score Function
32
1.14.4
Fisher Information
33
1.15
Convex Optimization and Duality
34
1.15.1
Lagrangian Method
3 6
1.15.2
Duality
37
Problems
41
References
46
2
Random Number, Random Variable, and Stochastic Process
Generation
49
2.1
Introduction
49
2.2
Random Number Generation
49
2.3
Random Variable Generation
51
2.3.1
Inverse-Transform Method
51
2.3.2
Alias Method
54
2.3.3
Composition Method
54
2.3.4
Acceptance-Rejection Method
55
2.4
Generating From Commonly Used Distributions
58
2.4.1
Generating Continuous Random Variables
58
2.4.2
Generating Discrete Random Variables
63
2.5
Random Vector Generation
65
2.5.1
Vector Acceptance-Rejection Method
66
2.5.2
Generating Variables from
a
Multinormal
Distribution
67
2.5.3
Generating Uniform Random Vectors Over a Simplex
68
2.5.4
Generating Random Vectors Uniformly Distributed Over a Unit
Hyperball and Hypersphere
69
2.5.5
Generating Random Vectors Uniformly Distributed Over a
Hyperellipsoid
70
2.6
Generating
Poisson
Processes
70
2.7
Generating Markov Chains and Markov Jump Processes
72
2.7.1
Random Walk on a Graph
72
2.7.2
Generating Markov Jump Processes
73
2.8
Generating Random Permutations
74
Problems
75
References
80
CONTENTS
ЇХ
3 Simulation
of Discrete-Event Systems
81
3.1
Simulation Models
82
3.1.1
Classification of Simulation Models
84
3.2
Simulation Clock and Event List for DEDS
85
3.3
Discrete-Event Simulation
87
3.3.1
Tandem Queue
87
3.3.2
Repairman Problem
91
Problems
94
References
96
4
Statistical Analysis of Discrete-Event Systems
97
4.1
Introduction
97
4.2
Static Simulation Models
98
4.2.1
Confidence Interval
100
4.3
Dynamic Simulation Models
101
4.3.1
Finite-Horizon Simulation
102
4.3.2
Steady-State Simulation
103
4.4
The Bootstrap Method
113
Problems
115
References
118
5
Controlling the Variance
119
5.1
Introduction
119
5.2
Common and Antithetic Random Variables
120
5.3
Control Variables
123
5.4
Conditional Monte Carlo
125
5.4.1
Variance Reduction for Reliability Models
126
5.5
Stratified Sampling
129
5.6
Importance Sampling
131
5.6.1
Weighted Samples
132
5.6.2
The Variance Minimization Method
132
5.6.3
The Cross-Entropy Method
136
5.7
Sequential Importance Sampling
141
5.7.1
Nonlinear Filtering for Hidden Markov Models
144
5.8
The Transform Likelihood Ratio Method
148
5.9
Preventing the Degeneracy of Importance Sampling
і
51
5.9.1
The Two-Stage Screening Algorithm
153
5.9.2
CaseStudy
158
Problems
161
References
165
6.1
Introduction
6.2
The Metropolis-Hastings Algorithm
6.3
The Hit-and-Run Sampler
6.4
The Gibbs Sampler
6.5
Ising and Potts Models
6.5.1
Ising Model
6.5.2
Potts Model
6.6
Bayesian Statistics
6.7
*
Other Markov Samplers
6.7.1
Slice Sampler
6.7.2
Reversible Jump Sampler
6.8
Simulated Annealing
6.9
Perfect Sampling
Problems
References
X
CONTENTS
6
Markov Chain
Monte Cario 167
167
168
173
175
178
178
179
181
183
185
186
189
192
194
199
Sensitivity Analysis and Monte Carlo Optimization
201
7.1
Introduction
201
7.2
The Score Function Method for Sensitivity Analysis of
DESS
203
7.3
Simulation-Based Optimization of
DESS
211
7.3.1
Stochastic Approximation
212
7.3.2
The Stochastic Counterpart Method
215
7.4
Sensitivity Analysis of DEDS
225
Problems
230
References
233
The Cross-Entropy Method
235
8.1
Introduction
235
8.2
Estimation of Rare-Event Probabilities
236
8.2.1
The Root-Finding Problem
245
8.2.2
The Screening Method for Rare Events
245
8.3
The
CE
Method for Optimization
249
8.4
The Max-cut Problem
253
8.5
The Partition Problem
259
8.5.1
Empirical Computational Complexity
260
8.6
The Traveling Salesman Problem
260
8.6.1
Incomplete Graphs
265
8.6.2
Node Placement
266
8.6.3
CaseStudies
267
8.7
Continuous Optimization
268
CONTENTS
XI
8.8
Noisy Optimization
269
Problems
271
References
275
9
Counting via Monte Carlo
279
9.1
Counting Problems
279
9.2
Satisfiability Problem
280
9.2.1
Random
АГ
-SAT
(AT-RSAT)
283
9.3
The Rare-Event Framework for Counting
284
9.3.1
Rare Events for the Satisfiability Problem
287
9.4
Other Randomized Algorithms for Counting
288
9.4.1
ЭС*
is a Union of Some Sets
291
9.4.2
Complexity of Randomized Algorithms: FPRAS and FPAUS
294
9.4.3
FPRAS for SATs in CNF
297
9.5
MinxEnt and Parametric MinxEnt
297
9.5.1
The MinxEnt Method
297
9.5.2
Rare-Event Probability Estimation Using
PME
301
9.6
PME
for Combinatorial Optimization Problems and Decision Making
306
9.7
Numerical Results
307
Problems
311
References
312
Appendix
315
A.
1
Cholesky Square Root Method
315
A.2 Exact Sampling from a Conditional Bernoulli Distribution
316
A.3 Exponential Families
317
A.4 Sensitivity Analysis
320
A.4.1 Convexity Results
321
A.4.2
Monotonicity
Results
322
A.5 A Simple
CE
Algorithm for Optimizing the Peaks Function
323
A.6 Discrete-time
Kalman
Filter
323
A.7 Bernoulli Disruption Problem
324
A.8 Complexity of Stochastic Programming Problems
326
Problems
334
References
335
Abbreviations and Acronyms
336
List of Symbols
338
Index
341 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Rubinstein, Reuven Y. 1938-2012 Kroese, Dirk P. 1963- |
| author_GND | (DE-588)131523341 (DE-588)137690320 |
| author_facet | Rubinstein, Reuven Y. 1938-2012 Kroese, Dirk P. 1963- |
| author_role | aut aut |
| author_sort | Rubinstein, Reuven Y. 1938-2012 |
| author_variant | r y r ry ryr d p k dp dpk |
| building | Verbundindex |
| bvnumber | BV023114683 |
| callnumber-first | Q - Science |
| callnumber-label | QA298 |
| callnumber-raw | QA298 |
| callnumber-search | QA298 |
| callnumber-sort | QA 3298 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 239 SK 820 SK 830 SK 840 SK 845 |
| classification_tum | MAT 629f |
| ctrlnum | (OCoLC)263724776 (DE-599)BVBBV023114683 |
| dewey-full | 518/.282 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518/.282 |
| dewey-search | 518/.282 |
| dewey-sort | 3518 3282 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV023114683 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:49:36Z |
| indexdate | 2024-07-09T21:11:21Z |
| institution | BVB |
| isbn | 9780470177945 |
| language | English |
| lccn | 2007029068 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016317217 |
| oclc_num | 263724776 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-N2 DE-384 DE-92 DE-634 DE-M382 DE-83 DE-11 DE-739 DE-578 |
| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-N2 DE-384 DE-92 DE-634 DE-M382 DE-83 DE-11 DE-739 DE-578 |
| physical | XVII, 345 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Rubinstein, Reuven Y. 1938-2012 Verfasser (DE-588)131523341 aut Simulation and the Monte Carlo method Reuven Y. Rubinstein ; Dirk P. Kroese 2. ed. Hoboken, N.J. Wiley 2008 XVII, 345 S. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Includes index. Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences." "Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method. Monte Carlo method Digital computer simulation Computersimulation (DE-588)4148259-1 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Diskretes Ereignissystem (DE-588)4196828-1 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Simulation (DE-588)4055072-2 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 s Diskretes Ereignissystem (DE-588)4196828-1 s Statistik (DE-588)4056995-0 s 1\p DE-604 Computersimulation (DE-588)4148259-1 s 2\p DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s 3\p DE-604 Simulation (DE-588)4055072-2 s 4\p DE-604 Kroese, Dirk P. 1963- Verfasser (DE-588)137690320 aut Erscheint auch als Online-Ausgabe 978-0-470-23038-1 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016317217&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rubinstein, Reuven Y. 1938-2012 Kroese, Dirk P. 1963- Simulation and the Monte Carlo method Monte Carlo method Digital computer simulation Computersimulation (DE-588)4148259-1 gnd Statistik (DE-588)4056995-0 gnd Diskretes Ereignissystem (DE-588)4196828-1 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Simulation (DE-588)4055072-2 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4148259-1 (DE-588)4056995-0 (DE-588)4196828-1 (DE-588)4240945-7 (DE-588)4055072-2 (DE-588)4064324-4 |
| title | Simulation and the Monte Carlo method |
| title_auth | Simulation and the Monte Carlo method |
| title_exact_search | Simulation and the Monte Carlo method |
| title_exact_search_txtP | Simulation and the Monte Carlo method |
| title_full | Simulation and the Monte Carlo method Reuven Y. Rubinstein ; Dirk P. Kroese |
| title_fullStr | Simulation and the Monte Carlo method Reuven Y. Rubinstein ; Dirk P. Kroese |
| title_full_unstemmed | Simulation and the Monte Carlo method Reuven Y. Rubinstein ; Dirk P. Kroese |
| title_short | Simulation and the Monte Carlo method |
| title_sort | simulation and the monte carlo method |
| topic | Monte Carlo method Digital computer simulation Computersimulation (DE-588)4148259-1 gnd Statistik (DE-588)4056995-0 gnd Diskretes Ereignissystem (DE-588)4196828-1 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Simulation (DE-588)4055072-2 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Monte Carlo method Digital computer simulation Computersimulation Statistik Diskretes Ereignissystem Monte-Carlo-Simulation Simulation Wahrscheinlichkeitsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016317217&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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