Handbook of Monte Carlo methods:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2011
|
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes index. -- "The purpose of this handbook is to provide an accessible and comprehensive compendium of Monte Carlo techniques and related topics. It contains a mix of theory (summarized), algorithms (pseudo and actual), and applications. Since the audience is broad, the theory is kept to a minimum, this without sacrificing rigor. The book is intended to be used as an essential guide to Monte Carlo methods to quickly look up ideas, procedures, formulas, pictures, etc., rather than purely a monograph for researchers or a textbook for students. As the popularity of these methods continues to grow, and new methods are developed in rapid succession, the staggering number of related techniques, ideas, concepts and algorithms makes it difficult to maintain an overall picture of the Monte Carlo approach. This book attempts to encapsulate the emerging dynamics of this field of study"-- Provided by publisher. |
| Physical Description: | XIX, 743 S. Ill., graph. Darst. |
| ISBN: | 9780470177938 |
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| 100 | 1 | |a Kroese, Dirk P. |d 1963- |e Verfasser |0 (DE-588)137690320 |4 aut | |
| 245 | 1 | 0 | |a Handbook of Monte Carlo methods |c Dirk P. Kroese ; Thomas Taimre ; Zdravko I. Botev |
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2011 | |
| 300 | |a XIX, 743 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in probability and statistics | |
| 500 | |a Includes index. -- "The purpose of this handbook is to provide an accessible and comprehensive compendium of Monte Carlo techniques and related topics. It contains a mix of theory (summarized), algorithms (pseudo and actual), and applications. Since the audience is broad, the theory is kept to a minimum, this without sacrificing rigor. The book is intended to be used as an essential guide to Monte Carlo methods to quickly look up ideas, procedures, formulas, pictures, etc., rather than purely a monograph for researchers or a textbook for students. As the popularity of these methods continues to grow, and new methods are developed in rapid succession, the staggering number of related techniques, ideas, concepts and algorithms makes it difficult to maintain an overall picture of the Monte Carlo approach. This book attempts to encapsulate the emerging dynamics of this field of study"-- Provided by publisher. | ||
| 650 | 4 | |a Monte Carlo method | |
| 650 | 7 | |a MATHEMATICS / Probability & Statistics / General |2 bisacsh | |
| 650 | 0 | 7 | |a Monte-Carlo-Simulation |0 (DE-588)4240945-7 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Taimre, Thomas |d 1983- |e Verfasser |0 (DE-588)1013624416 |4 aut | |
| 700 | 1 | |a Botev, Zdravko I. |d 1982- |e Verfasser |0 (DE-588)1011448882 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-021104143 | ||
Record in the Search Index
| _version_ | 1804143775158632448 |
|---|---|
| adam_text | CONTENTS
Preface
xvii
Acknowledgments
xix
1
Uniform Random Number Generation
1
1.1
Random Numbers
1
1.1.1
Properties of a Good Random Number Generator
2
1.1.2
Choosing a Good Random Number Generator
3
1.2
Generators Based on Linear Recurrences
4
1.2.1
Linear Congruential Generators
4
1.2.2
Multiple-Recursive Generators
5
1.2.3
Matrix Congruential Generators
6
1.2.4
Modulo
2
Linear Generators
6
1.3
Combined Generators
8
1.4
Other Generators
10
1.5
Tests for Random Number Generators
11
1.5.1
Spectral Test
12
1.5.2
Empirical Tests
14
References
21
VIII CONTENTS
2
Quasirandom Number
Generation
2.1
Multidimensional
Integration
2.2 Van der Corput and Digital
Sequences
2.3
Halton
Sequences
2.4
Faure
Sequences
2.5
Sobol
Sequences
2.6
Lattice Methods
2.7
Randomization and Scrambling
References
3
Random Variable Generation
43
3.1
Generic Algorithms Based on Common Transformations
44
3.1.1
Inverse-Transform Method
45
3.1.2
Other Transformation Methods
47
3.1.3
Table Lookup Method
55
3.1.4
Alias Method
56
3.1.5
Acceptance-Rejection Method
59
3.1.6
Ratio of Uniforms Method
66
3.2
Generation Methods for Multivariate Random Variables
67
3.2.1
Copulas
68
3.3
Generation Methods for Various Random Objects
70
3.3.1
Generating Order Statistics
70
3.3.2
Generating Uniform Random Vectors in a Simplex
71
3.3.3
Generating Random Vectors Uniformly Distributed in
a Unit Hyperball and Hypersphere
74
3.3.4
Generating Random Vectors Uniformly Distributed in
a Hyperellipsoid
75
3.3.5
Uniform Sampling on a Curve
75
3.3.6
Uniform Sampling on a Surface
76
3.3.7
Generating Random Permutations
79
3.3.8
Exact Sampling From a Conditional Bernoulli
Distribution
80
References
83
4
Probability Distributions
85
4.1
Discrete Distributions
85
4.1.1
Bernoulli Distribution
85
4.1.2
Binomial Distribution
86
4.1.3
Geometric Distribution
91
4.1.4
Hypergeometric Distribution
93
4.1.5
Negative Binomial Distribution
94
4.1.6
Phase-Type Distribution
(Discrete Case)
96
4.1.7
Poisson
Distribution
98
4.1.8
Uniform Distribution (Discrete Case)
101
4.2
Continuous Distributions
102
4.2.1
Beta Distribution
102
4.2.2
Cauchy Distribution
106
4.2.3
Exponential Distribution
108
4.2.4
F
Distribution
109
4.2.5
Frédiét
Distribution 111
4.2.6
Gamma Distribution
112
4.2.7
G
umbel Distribution
116
4.2.8
Laplace Distribution
118
4.2.9
Logistic Distribution
119
4.2.10
Log-Normal Distribution
120
4.2.11
Normal Distribution
122
4.2.12
Pareto Distribution
125
4.2.13
Phase-Type Distribution (Continuous Case)
126
4.2.14
Stable Distribution
129
4.2.15
Student s
t
Distribution
131
4.2.16
Uniform Distribution (Continuous Case)
134
4.2.17 Wald
Distribution
135
4.2.18
Weibull Distribution
137
4.3
Multivariate Distributions
138
4.3.1
Dirichlet Distribution
139
4.3.2
Multinomial Distribution
141
4.3.3
Multivariate Normal Distribution
143
4.3.4
Multivariate Student s
t
Distribution
147
4.3.5
Wishart
Distribution
148
References
150
Random Process Generation
153
5.1
Gaussian Processes
154
5.1.1
Markovian Gaussian Processes
159
5.1.2
Stationary Gaussian Processes and the FFT
160
5.2
Markov Chains
162
5.3
Markov Jump Processes
166
5.4
Poisson
Processes
170
5.4.1
Compound
Poisson
Process
174
5.5
Wiener Process and Brownian Motion
177
5.6
Stochastic Differential Equations and Diffusion Processes
183
5.6.1
Eulers
Method
185
5.6.2
Milstein s Method
187
5.6.3
Implicit
Euler
188
5.6.4
Exact
Methods
189
5.6.5
Error and Accuracy
191
5.7
Brownian Bridge
193
5.8
Geometric Brownian Motion
196
5.9
Ornstein-Uhlenbeck Process
198
5.10
Reflected Brownian Motion
200
5.11
Fractional Brownian Motion
203
5.12
Random Fields
206
5.13
Levy Processes
208
5.13.1
Increasing Levy Processes
211
5.13.2
Generating Levy Processes
214
5.14
Time Series
219
References
222
Markov Chain Monte Carlo
225
6.1
Metropolis-Hastings Algorithm
226
6.1.1
Independence Sampler
227
6.1.2
Random Walk Sampler
230
6.2
Gibbs Sampler
233
6.3
Specialized Samplers
240
6.3.1
Hit-and-Run Sampler
240
6.3.2
Shake-and-Bake Sampler
251
6.3.3
Metropolis-Gibbs Hybrids
256
6.3.4
Multiple-Try Metropolis-Hastings
257
6.3.5
Auxiliary Variable Methods
259
6.3.6
Reversible Jump Sampler
269
6.4
Implementation Issues
273
6.5
Perfect Sampling
274
References
276
Discrete Event Simulation
281
7.1
Simulation Models
281
7.2
Discrete Event Systems
283
7.3
Event-Oriented Approach
285
7.4
More Examples of Discrete Event Simulation
289
7.4.1
Inventory System
289
7.4.2
Tandem Queue
293
7.4.3
Repairman Problem
296
References
300
Statistical Analysis of Simulation Data
301
8.1
Simulation Data
301
8.1.1
Data Visualization
302
8.1.2
Data Summarization
303
8.2
Estimation of Performance Measures for Independent Data
305
8.2.1
Delta Method
308
8.3
Estimation of Steady-State Performance Measures
309
8.3.1
Covariance Method
309
8.3.2
Batch Means Method
311
8.3.3
Regenerative Method
313
8.4
Empirical Cdf
316
8.5
Kernel Density Estimation
319
8.5.1
Least Squares Cross Validation
321
8.5.2
Plug-in Bandwidth Selection
326
8.6
Resampling and the Bootstrap Method
331
Λ
7
Goodness of Fit
333
8.7.1
Graphical Procedures
334
8.7.2
Kolmogorov-Smirnov Test
336
8.7.3
Anderson-Darling Test
339
8.7.4
χ2
Tests
340
References
343
Variance Reduction
347
9.1
Variance Reduction Example
348
9.2
Antithetic Random Variables
349
9.3
Control Variables
351
9.4
Conditional Monte Carlo
354
9.5
Stratified Sampling
356
9.6
Latin Hypercube Sampling
360
9.7
Importance Sampling
362
9.7.1
Minimum-Variance Density
363
9.7.2
Variance Minimization Method
364
9.7.3
Cross-Entropy Method
366
9.7.4
Weighted Importance Sampling
368
9.7.5
Sequential Importance Sampling
369
9.7.6
Response Surface Estimation via Importance Sampling
373
9.8
Quasi Monte Carlo
376
References
379
10
Rare-Event Simulation
381
10.1
Efficiency of Estimators
382
10.2
Importance Sampling Methods for Light Tails
385
10.2.1
Estimation of Stopping Time Probabilities
386
10.2.2
Estimation of Overflow Probabilities
389
10.2.3
Estimation For Compound
Poisson
Sums
391
10.3
Conditioning Methods for Heavy Tails
393
10.3.1
Estimation for Compound Sums
394
10.3.2
Sum of Nonidentically Distributed Random Variables
396
10.4
State-Dependent Importance Sampling
398
10.5
Cross-Entropy Method for Rare-Event Simulation
404
10.6
Splitting Method
409
References
416
11
Estimation of Derivatives
421
11.1
Gradient Estimation
11.2
Finite Difference Method
11.3
Infinitesimal
Perturbation Analysis
11.4
Score Function Method
11.4.1
Score Function Method With Importance Sampling
11.5
Weak Derivatives
11.6
Sensitivity Analysis for Regenerative Processes
References
12
Randomized Optimization
441
12.1
Stochastic Approximation
441
12.2
Stochastic Counterpart Method
446
12.3
Simulated Annealing
449
12.4
Evolutionary Algorithms
452
12.4.1
Genetic Algorithms
452
12.4.2
Differential Evolution
454
12.4.3
Estimation of Distribution Algorithms
456
12.5
Cross-Entropy Method for Optimization
457
12.6
Other Randomized Optimization Techniques
460
References
461
13
Cross-Entropy Method
463
13.1
Cross-Entropy Method
13.2
Cross-Entropy Method for Estimation
13.3
Cross-Entropy Method for Optimization
13.3.1
Combinatorial Optimization
13.3.2
Continuous Optimization
471
13.3.3
Constrained Optimization
473
13.3.4
Noisy Optimization
476
References
477
14
Particle Methods
481
14.1
Sequential Monte Carlo
482
14.2
Particle Splitting
485
14.3
Splitting for Static Rare-Event Probability Estimation
486
14.4
Adaptive Splitting Algorithm
493
14.5
Estimation of Multidimensional Integrals
495
14.6
Combinatorial Optimization via Splitting
504
14.6.1
Knapsack Problem
505
14.6.2
Traveling Salesman Problem
506
14.6.3
Quadratic Assignment Problem
508
14.7
Markov Chain Monte Carlo With Splitting
509
References
517
15
Applications to Finance
521
15.1
Standard Model
521
15.2
Pricing via Monte Carlo Simulation
526
15.3
Sensitivities
538
15.3.1
Pathwise Derivative Estimation
540
15.3.2
Score Function Method
542
References
546
16
Applications to Network Reliability
549
16.1
Network Reliability
549
16.2
Evolution Model for a Static Network
551
16.3
Conditional Monte Carlo
554
16.3.1
Leap-Evolve Algorithm
560
16.4
Importance Sampling for Network Reliability
562
16.4.1
Importance Sampling Using Bounds
562
16.4.2
Importance Sampling With Conditional Monte Carlo
565
16.5
Splitting Method
567
16.5.1
Acceleration Using Bounds
573
References
574
17
Applications to Differential Equations
577
17.1
Connections Between Stochastic and Partial Differential
Equations
577
17.1.1
Boundary Value Problems
579
17.1.2
Terminal Value Problems
584
17.1.3
Terminal-Boundary Problems
585
17.2
Transport Processes and Equations
587
17.2.1
Application to Transport Equations
589
17.2.2
Boltzmann Equation
593
17.3
Connections to ODEs Through Scaling
597
References
602
Appendix A: Probability and Stochastic Processes
605
A.I Random Experiments and Probability Spaces
605
A.
1.1
Properties of a Probability Measure
607
A.
2
Random Variables and Probability Distributions
607
A.
2.1
Probability Density
610
A.
2.2
Joint Distributions
611
A.3 Expectation and Variance
612
A.
3.1
Properties of the Expectation
614
A.
3.2
Variance
615
A.
4
Conditioning and Independence
616
A.
4.1
Conditional Probability
616
A.
4.2
Independence
616
A.
4.3
Covariance
617
A.
4.4
Conditional Density and Expectation
618
A.5 LP Space
619
A.
6
Functions of Random Variables
620
A.
6.1
Linear Transformations
620
A.
6.2
General Transformations
620
A.
7
Generating Function and Integral Transforms
621
A.
7.1
Probability Generating Function
621
A.
7.2
Moment Generating Function and Laplace Transform
621
A.
7.3
Characteristic Function
622
A.
8
Limit Theorems
623
A.
8.1
Modes of Convergence
623
A.
8.2
Converse Results on Modes of Convergence
624
A.
8.3
Law of Large Numbers and Central Limit Theorem
625
A.
9
Stochastic Processes
626
A.
9.1
Gaussian Property
627
A.9.2 Markov Property
628
A.
9.3
Martingale Property
629
A.
9.4
Regenerative Property
630
A.
9.5
Stationarity and Reversibility
631
A.
10
Markov Chains
632
Α.
10.1
Classification
of States
633
A.
10.2
Limiting Behavior
633
A.10.3 Reversibility
635
A.
11
Markov Jump Processes
635
A.
11.1
Limiting Behavior
638
A.
12
Ito
Integral and
Ito
Processes
639
A.
13
Diffusion Processes
643
A.
13.1
Kolmogorov Equations
646
A.
13.2
Stationary Distribution
648
A.
13.3
Feynman-Kac Formula
648
A.
13.4
Exit Times
649
References
650
Appendix B: Elements of Mathematical Statistics
653
B.I Statistical Inference
653
B.I.I Classical Models
654
B.1.2 Sufficient Statistics
655
B.1.3 Estimation
656
B.I.
4
Hypothesis Testing
660
B.2 Likelihood
664
B.2.1 Likelihood Methods for Estimation
667
B.2.
2
Numerical Methods for Likelihood Maximization
669
B.2.3 Likelihood Methods for Hypothesis Testing
671
B.3 Bayesian Statistics
672
B.3.1 Conjugacy
675
References
676
Appendix C: Optimization
677
C.I Optimization Theory
677
C.I.I Lagrangian Method
683
C.1.2 Duality
684
C.2 Techniques for Optimization
685
C.2.1 Transformation of Constrained Problems
685
C.2.
2
Numerical Methods for Optimization and Root Finding
687
C.3 Selected Optimization Problems
694
C.3.1 Satisfiability Problem
694
C.3.
2
Knapsack Problem
694
C.3.3 Max-Cut Problem
695
C.3.
4
Traveling Salesman Problem
695
C.3.
5
Quadratic Assignment Problem
695
C.3.6 Clustering Problem
696
С.
4
Continuous Problems
696
С.
4.1
Unconstrained Problems
696
C.4.2 Constrained Problems
697
References
699
Appendix D: Miscellany
701
D.I Exponential Families
701
D.2 Properties of Distributions
703
D.2.1 Tail Properties
703
D.2.
2
Stability Properties
705
D.3 Cholesky Factorization
706
D.4 Discrete Fourier Transform. FFT. and
Circulant
Matrices
706
D.5 Discrete Cosine Transform
708
D.6 Differentiation
709
D.7 Expectation-Maximization (EM) Algorithm
711
D.8
Poisson
Summation Formula
714
D.9 Special Functions
715
D.9.1 Beta Function
Β (α, β)
715
D.
9.2
Incomplete Beta Function Ix
(α, β)
715
D.
9.3
Error Function
егі(ж)
715
D.
9.4
Digamma
function
φ (χ)
716
D.9.5 Gamma Function
Г (а)
716
D.
9.6
Incomplete Gamma Function
Ρ
(a, x)
716
D.9.
7
Hypergeometric Function 2-F1 (a, b; c: z)
716
D.9.
8
Confluent Hypergeometric Function iFi(q;
7;
ж)
717
D.
9.9
Modified Bessel Function of the Second Kind Kv{x)
717
References
717
Acronyms and Abbreviations
719
List of Symbols
721
List of Distributions
724
Index
727
|
| any_adam_object | 1 |
| author | Kroese, Dirk P. 1963- Taimre, Thomas 1983- Botev, Zdravko I. 1982- |
| author_GND | (DE-588)137690320 (DE-588)1013624416 (DE-588)1011448882 |
| author_facet | Kroese, Dirk P. 1963- Taimre, Thomas 1983- Botev, Zdravko I. 1982- |
| author_role | aut aut aut |
| author_sort | Kroese, Dirk P. 1963- |
| author_variant | d p k dp dpk t t tt z i b zi zib |
| building | Verbundindex |
| bvnumber | BV037189703 |
| 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 |
| classification_tum | MAT 629f |
| ctrlnum | (OCoLC)846108259 (DE-599)BVBBV037189703 |
| 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 |
| format | Book |
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| id | DE-604.BV037189703 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:53:01Z |
| institution | BVB |
| isbn | 9780470177938 |
| language | English |
| lccn | 2010042348 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021104143 |
| oclc_num | 846108259 |
| open_access_boolean | |
| owner | DE-20 DE-739 DE-824 DE-11 DE-91G DE-BY-TUM DE-19 DE-BY-UBM |
| owner_facet | DE-20 DE-739 DE-824 DE-11 DE-91G DE-BY-TUM DE-19 DE-BY-UBM |
| physical | XIX, 743 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Kroese, Dirk P. 1963- Verfasser (DE-588)137690320 aut Handbook of Monte Carlo methods Dirk P. Kroese ; Thomas Taimre ; Zdravko I. Botev Hoboken, NJ Wiley 2011 XIX, 743 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Includes index. -- "The purpose of this handbook is to provide an accessible and comprehensive compendium of Monte Carlo techniques and related topics. It contains a mix of theory (summarized), algorithms (pseudo and actual), and applications. Since the audience is broad, the theory is kept to a minimum, this without sacrificing rigor. The book is intended to be used as an essential guide to Monte Carlo methods to quickly look up ideas, procedures, formulas, pictures, etc., rather than purely a monograph for researchers or a textbook for students. As the popularity of these methods continues to grow, and new methods are developed in rapid succession, the staggering number of related techniques, ideas, concepts and algorithms makes it difficult to maintain an overall picture of the Monte Carlo approach. This book attempts to encapsulate the emerging dynamics of this field of study"-- Provided by publisher. Monte Carlo method MATHEMATICS / Probability & Statistics / General bisacsh Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 s b DE-604 Taimre, Thomas 1983- Verfasser (DE-588)1013624416 aut Botev, Zdravko I. 1982- Verfasser (DE-588)1011448882 aut Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021104143&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kroese, Dirk P. 1963- Taimre, Thomas 1983- Botev, Zdravko I. 1982- Handbook of Monte Carlo methods Monte Carlo method MATHEMATICS / Probability & Statistics / General bisacsh Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| subject_GND | (DE-588)4240945-7 |
| title | Handbook of Monte Carlo methods |
| title_auth | Handbook of Monte Carlo methods |
| title_exact_search | Handbook of Monte Carlo methods |
| title_full | Handbook of Monte Carlo methods Dirk P. Kroese ; Thomas Taimre ; Zdravko I. Botev |
| title_fullStr | Handbook of Monte Carlo methods Dirk P. Kroese ; Thomas Taimre ; Zdravko I. Botev |
| title_full_unstemmed | Handbook of Monte Carlo methods Dirk P. Kroese ; Thomas Taimre ; Zdravko I. Botev |
| title_short | Handbook of Monte Carlo methods |
| title_sort | handbook of monte carlo methods |
| topic | Monte Carlo method MATHEMATICS / Probability & Statistics / General bisacsh Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| topic_facet | Monte Carlo method MATHEMATICS / Probability & Statistics / General Monte-Carlo-Simulation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021104143&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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