Approximating integrals via Monte Carlo and deterministic methods:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford Univ. Press
2000
|
| Edition: | 1. publ. |
| Series: | Oxford statistical science series
20 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 288 S. |
| ISBN: | 0198502788 9780198502784 |
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MARC
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| 100 | 1 | |a Evans, Michael |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Approximating integrals via Monte Carlo and deterministic methods |c Michael Evans ; Tim Swartz |
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Record in the Search Index
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| adam_text | Contents
1 Introduction 1
1.1 The problem 1
1.2 The dimensional effect 4
1.3 Examples 7
1.4 Outline of the book and additional relevant references 13
1.5 Exercises 15
2 Some basic concepts 17
2.1 Introduction 17
2.2 Exact or symbolic integration 17
2.3 Integrability 18
2.4 Reparameterization 19
2.5 Multimodality and shape 21
2.6 Error analysis 22
2.6.1 Absolute and relative error 23
2.6.2 Round off error 25
2.6.3 Interval analysis 27
2.7 Software 27
2.8 Exercises 28
3 Algorithms for sampling 30
3.1 Introduction 30
3.2 Generating uniform random variables 31
3.2.1 Randomness 31
3.2.2 Pseudo random sequences of uniforms 31
3.2.3 Linear congruential generators 33
3.2.4 Other generators 35
3.3 Inversion methods for random variables 36
3.4 Rejection methods for random variables 38
3.5 Hit or miss integration 40
3.6 Adaptive rejection methods 41
3.7 Specialized methods 47
3.8 Generating from multivariate distributions 49
3.9 Exercises 52
viii CONTENTS
4 Asymptotic approximations 54
4.1 Introduction 54
4.2 Asymptotic expansions 55
4.3 Approximating one dimensional integrals 57
4.3.1 Integration by parts 57
4.3.2 Watson s lemma 59
4.3.3 Laplace s approximation 62
4.3.4 Saddle point approximations 71
4.3.5 Edgeworth expansions 78
4.4 Approximating multidimensional integrals 86
4.5 Exercises 95
5 Multiple quadrature 98
5.1 Introduction 98
5.2 Multiple quadrature rules 98
5.3 Interpolatory rules on Rl 101
5.3.1 Rectangle rules 107
5.3.2 The midpoint rule 108
5.3.3 Newton Cotes rules 108
5.3.4 Gauss rules 110
5.3.5 Error in interpolatory rules 116
5.4 Envelope rules and exact error analysis 117
5.5 Product rules 124
5.6 Monomial rules 132
5.7 Bayesian quadrature 137
5.8 Quasi random rules 143
5.9 Lattice rules 152
5.10 Adaptive quadrature 156
5.10.1 Adaptive Romberg integration 157
5.10.2 Gauss Kronrod rules 158
5.10.3 Adaptive product Hermite rules 159
5.10.4 Subregion adaptive integration 160
5.11 Exercises 161
6 Independent importance sampling 165
6.1 Introduction 165
6.2 The independent importance sampling algorithm 166
6.3 Choosing an importance sampler 175
6.4 Variance reduction methods 182
6.4.1 Dimension reduction 182
6.4.2 Stratified sampling 183
6.4.3 Ermakov Zolotukin sampling 188
6.4.4 Systematic sampling 190
CONTENTS ix
6.4.5 Randomized quadrature 202
6.4.6 Control variates 206
6.5 Adaptive importance sampling 209
6.6 Exercises 221
7 Markov chain methods 225
7.1 Introduction 225
7.2 Markov chains 226
7.3 Markov chain sampling algorithms 232
7.3.1 Metropolis chains 223
7.3.2 Gibbs sampling 236
7.3.3 Hybrid chains 241
7.3.4 Hit and run chains 243
7.3.5 Slice sampling 244
7.3.6 Perfect sampling 245
7.4 Related techniques and issues 248
7.4.1 Reparameterization 248
7.4.2 Importance sampling 250
7.4.3 Variance reduction techniques 251
7.4.4 Simulated tempering 252
7.4.5 Estimating normalizing constants and ratios of
normalizing constants 254
7.5 Assessing convergence and error 257
7.5.1 Diagnostics for stationarity 258
7.5.2 Estimating the asymptotic variance 261
7.6 Web resources and software 263
7.7 Exercises 264
References 266
Author index 281
Subject index 285
|
| any_adam_object | 1 |
| author | Evans, Michael Swartz, Tim 1958- |
| author_GND | (DE-588)143975625 |
| author_facet | Evans, Michael Swartz, Tim 1958- |
| author_role | aut aut |
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| author_variant | m e me t s ts |
| building | Verbundindex |
| bvnumber | BV013217674 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.43 |
| dewey-search | 515/.43 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV013217674 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:41:52Z |
| institution | BVB |
| isbn | 0198502788 9780198502784 |
| language | English |
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| physical | IX, 288 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | Oxford Univ. Press |
| record_format | marc |
| series | Oxford statistical science series |
| series2 | Oxford statistical science series |
| spelling | Evans, Michael Verfasser aut Approximating integrals via Monte Carlo and deterministic methods Michael Evans ; Tim Swartz 1. publ. Oxford Oxford Univ. Press 2000 IX, 288 S. txt rdacontent n rdamedia nc rdacarrier Oxford statistical science series 20 Approximation, Théorie de l' Benaderingen (wiskunde) gtt Calcul intégral Integraalrekening gtt Monte Carlo-methode gtt Monte-Carlo, Méthode de Numerieke methoden gtt Approximation theory Calculus, Integral Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf Integralrechnung (DE-588)4027232-1 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Integralgleichung (DE-588)4027229-1 s Randwertproblem (DE-588)4048395-2 s Monte-Carlo-Simulation (DE-588)4240945-7 s DE-604 Approximationstheorie (DE-588)4120913-8 s Integralrechnung (DE-588)4027232-1 s Swartz, Tim 1958- Verfasser (DE-588)143975625 aut Oxford statistical science series 20 (DE-604)BV001908661 20 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009006429&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Evans, Michael Swartz, Tim 1958- Approximating integrals via Monte Carlo and deterministic methods Oxford statistical science series Approximation, Théorie de l' Benaderingen (wiskunde) gtt Calcul intégral Integraalrekening gtt Monte Carlo-methode gtt Monte-Carlo, Méthode de Numerieke methoden gtt Approximation theory Calculus, Integral Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd Integralgleichung (DE-588)4027229-1 gnd Integralrechnung (DE-588)4027232-1 gnd Approximationstheorie (DE-588)4120913-8 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4240945-7 (DE-588)4027229-1 (DE-588)4027232-1 (DE-588)4120913-8 (DE-588)4048395-2 (DE-588)4113937-9 |
| title | Approximating integrals via Monte Carlo and deterministic methods |
| title_auth | Approximating integrals via Monte Carlo and deterministic methods |
| title_exact_search | Approximating integrals via Monte Carlo and deterministic methods |
| title_full | Approximating integrals via Monte Carlo and deterministic methods Michael Evans ; Tim Swartz |
| title_fullStr | Approximating integrals via Monte Carlo and deterministic methods Michael Evans ; Tim Swartz |
| title_full_unstemmed | Approximating integrals via Monte Carlo and deterministic methods Michael Evans ; Tim Swartz |
| title_short | Approximating integrals via Monte Carlo and deterministic methods |
| title_sort | approximating integrals via monte carlo and deterministic methods |
| topic | Approximation, Théorie de l' Benaderingen (wiskunde) gtt Calcul intégral Integraalrekening gtt Monte Carlo-methode gtt Monte-Carlo, Méthode de Numerieke methoden gtt Approximation theory Calculus, Integral Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd Integralgleichung (DE-588)4027229-1 gnd Integralrechnung (DE-588)4027232-1 gnd Approximationstheorie (DE-588)4120913-8 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Approximation, Théorie de l' Benaderingen (wiskunde) Calcul intégral Integraalrekening Monte Carlo-methode Monte-Carlo, Méthode de Numerieke methoden Approximation theory Calculus, Integral Monte Carlo method Monte-Carlo-Simulation Integralgleichung Integralrechnung Approximationstheorie Randwertproblem Hochschulschrift |
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