Simulation and the Monte Carlo Method

 
 
John Wiley & Sons Inc (Verlag)
  • 3. Auflage
  • |
  • erschienen am 20. Oktober 2016
  • |
  • 432 Seiten
 
E-Book | PDF mit Adobe DRM | Systemvoraussetzungen
978-1-118-63220-8 (ISBN)
 
This accessible new edition explores the major topics in Monte Carlo simulation that have arisen over the past 30 years and presents a sound foundation for problem solving
Simulation and the Monte Carlo Method, Third Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the state-of-the-art theory, methods and applications that have emerged in Monte Carlo simulation since the publication of the classic First Edition over more than a quarter of a century 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. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo, variance reduction techniques such as importance (re-)sampling, and the transform likelihood ratio method, the score function method for sensitivity analysis, the stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization, the cross-entropy method for rare events estimation and combinatorial optimization, and application of Monte Carlo techniques for counting problems. An extensive range of exercises is provided at the end of each chapter, as well as a generous sampling of applied examples.
The Third Edition features a new chapter on the highly versatile splitting method, with applications to rare-event estimation, counting, sampling, and optimization. A second new chapter introduces the stochastic enumeration method, which is a new fast sequential Monte Carlo method for tree search. In addition, the Third Edition features new material on:
* Random number generation, including multiple-recursive generators and the Mersenne Twister
* Simulation of Gaussian processes, Brownian motion, and diffusion processes
* Multilevel Monte Carlo method
* New enhancements of the cross-entropy (CE) method, including the "improved" CE method, which uses sampling from the zero-variance distribution to find the optimal importance sampling parameters
* Over 100 algorithms in modern pseudo code with flow control
* Over 25 new exercises
Simulation and the Monte Carlo Method, Third Edition is an excellent text for upper-undergraduate and beginning graduate courses in stochastic 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.
Reuven Y. Rubinstein, DSc, was Professor Emeritus in the Faculty of Industrial Engineering and Management at Technion-Israel Institute of Technology. He served as a consultant at numerous large-scale organizations, such as IBM, Motorola, and NEC. The author of over 100 articles and six books, Dr. Rubinstein was also the inventor of the popular score-function method in simulation analysis and generic cross-entropy methods for combinatorial optimization and counting.
Dirk P. Kroese, PhD, is a Professor of Mathematics and Statistics in the School of Mathematics and Physics of The University of Queensland, Australia. He has published over 100 articles and four books in a wide range of areas in applied probability and statistics, including Monte Carlo methods, cross-entropy, randomized algorithms, tele-traffic c theory, reliability, computational statistics, applied probability, and stochastic modeling.
weitere Ausgaben werden ermittelt
1 - SIMULATION AND THE MONTE CARLO METHOD [Seite 3]
2 - CONTENTS [Seite 9]
3 - PREFACE [Seite 15]
4 - ACKNOWLEDGMENTS [Seite 19]
5 - CHAPTER 1 PRELIMINARIES [Seite 21]
5.1 - 1.1 INTRODUCTION [Seite 21]
5.2 - 1.2 RANDOM EXPERIMENTS [Seite 21]
5.3 - 1.3 CONDITIONAL PROBABILITY AND INDEPENDENCE [Seite 22]
5.4 - 1.4 RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS [Seite 24]
5.5 - 1.5 SOME IMPORTANT DISTRIBUTIONS [Seite 25]
5.6 - 1.6 EXPECTATION [Seite 26]
5.7 - 1.7 JOINT DISTRIBUTIONS [Seite 27]
5.8 - 1.8 FUNCTIONS OF RANDOM VARIABLES [Seite 31]
5.8.1 - 1.8.1 Linear Transformations [Seite 32]
5.8.2 - 1.8.2 General Transformations [Seite 33]
5.9 - 1.9 TRANSFORMS [Seite 34]
5.10 - 1.10 JOINTLY NORMAL RANDOM VARIABLES [Seite 35]
5.11 - 1.11 LIMIT THEOREMS [Seite 36]
5.12 - 1.12 POISSON PROCESSES [Seite 37]
5.13 - 1.13 MARKOV PROCESSES [Seite 39]
5.13.1 - 1.13.1 Markov Chains [Seite 39]
5.13.2 - 1.13.2 Classification of States [Seite 41]
5.13.3 - 1.13.3 Limiting Behavior [Seite 42]
5.13.4 - 1.13.4 Reversibility [Seite 44]
5.13.5 - 1.13.5 Markov Jump Processes [Seite 45]
5.14 - 1.14 GAUSSIAN PROCESSES [Seite 47]
5.15 - 1.15 INFORMATION [Seite 48]
5.15.1 - 1.15.1 Shannon Entropy [Seite 49]
5.15.2 - 1.15.2 Kullback-Leibler Cross-Entropy [Seite 51]
5.15.3 - 1.15.3 Maximum Likelihood Estimator and Score Function [Seite 52]
5.15.4 - 1.15.4 Fisher Information [Seite 53]
5.16 - 1.16 CONVEX OPTIMIZATION AND DUALITY [Seite 54]
5.16.1 - 1.16.1 Lagrangian Method [Seite 55]
5.16.2 - 1.16.2 Duality [Seite 57]
5.17 - PROBLEMS [Seite 61]
5.18 - REFERENCES [Seite 66]
6 - CHAPTER 2 RANDOM NUMBER, RANDOM VARIABLE, AND STOCHASTIC PROCESS GENERATION [Seite 69]
6.1 - 2.1 INTRODUCTION [Seite 69]
6.2 - 2.2 RANDOM NUMBER GENERATION [Seite 69]
6.2.1 - 2.2.1 Multiple Recursive Generators [Seite 71]
6.2.2 - 2.2.2 Modulo 2 Linear Generators [Seite 72]
6.3 - 2.3 RANDOM VARIABLE GENERATION [Seite 75]
6.3.1 - 2.3.1 Inverse-Transform Method [Seite 75]
6.3.2 - 2.3.2 Alias Method [Seite 77]
6.3.3 - 2.3.3 Composition Method [Seite 78]
6.3.4 - 2.3.4 Acceptance-Rejection Method [Seite 79]
6.4 - 2.4 GENERATING FROM COMMONLY USED DISTRIBUTIONS [Seite 82]
6.4.1 - 2.4.1 Generating Continuous Random Variables [Seite 82]
6.4.2 - 2.4.2 Generating Discrete Random Variables [Seite 87]
6.5 - 2.5 RANDOM VECTOR GENERATION [Seite 90]
6.5.1 - 2.5.1 Vector Acceptance-Rejection Method [Seite 91]
6.5.2 - 2.5.2 Generating Variables from a Multinormal Distribution [Seite 92]
6.5.3 - 2.5.3 Generating Uniform Random Vectors over a Simplex [Seite 93]
6.5.4 - 2.5.4 Generating Random Vectors Uniformly Distributed over a Unit Hyperball and Hypersphere [Seite 94]
6.5.5 - 2.5.5 Generating Random Vectors Uniformly Distributed inside a Hyperellipsoid [Seite 95]
6.6 - 2.6 GENERATING POISSON PROCESSES [Seite 95]
6.7 - 2.7 GENERATING MARKOV CHAINS AND MARKOV JUMP PROCESSES [Seite 97]
6.7.1 - 2.7.1 Random Walk on a Graph [Seite 98]
6.7.2 - 2.7.2 Generating Markov Jump Processes [Seite 99]
6.8 - 2.8 GENERATING GAUSSIAN PROCESSES [Seite 100]
6.9 - 2.9 GENERATING DIFFUSION PROCESSES [Seite 101]
6.10 - 2.10 GENERATING RANDOM PERMUTATIONS [Seite 103]
6.11 - PROBLEMS [Seite 105]
6.12 - REFERENCES [Seite 109]
7 - CHAPTER 3 SIMULATION OF DISCRETE-EVENT SYSTEMS [Seite 111]
7.1 - 3.1 INTRODUCTION [Seite 111]
7.2 - 3.2 SIMULATION MODELS [Seite 112]
7.2.1 - 3.2.1 Classification of Simulation Models [Seite 114]
7.3 - 3.3 SIMULATION CLOCK AND EVENT LIST FOR DEDS [Seite 115]
7.4 - 3.4 DISCRETE-EVENT SIMULATION [Seite 117]
7.4.1 - 3.4.1 Tandem Queue [Seite 117]
7.4.2 - 3.4.2 Repairman Problem [Seite 121]
7.5 - PROBLEMS [Seite 123]
7.6 - REFERENCES [Seite 126]
8 - CHAPTER 4 STATISTICAL ANALYSIS OF DISCRETE-EVENT SYSTEMS [Seite 127]
8.1 - 4.1 INTRODUCTION [Seite 127]
8.2 - 4.2 ESTIMATORS AND CONFIDENCE INTERVALS [Seite 128]
8.3 - 4.3 STATIC SIMULATION MODELS [Seite 130]
8.4 - 4.4 DYNAMIC SIMULATION MODELS [Seite 132]
8.4.1 - 4.4.1 Finite-Horizon Simulation [Seite 134]
8.4.2 - 4.4.2 Steady-State Simulation [Seite 134]
8.5 - 4.5 BOOTSTRAP METHOD [Seite 146]
8.6 - PROBLEMS [Seite 147]
8.7 - REFERENCES [Seite 150]
9 - CHAPTER 5 CONTROLLING THE VARIANCE [Seite 153]
9.1 - 5.1 INTRODUCTION [Seite 153]
9.2 - 5.2 COMMON AND ANTITHETIC RANDOM VARIABLES [Seite 154]
9.3 - 5.3 CONTROL VARIABLES [Seite 157]
9.4 - 5.4 CONDITIONAL MONTE CARLO [Seite 159]
9.4.1 - 5.4.1 Variance Reduction for Reliability Models [Seite 161]
9.5 - 5.5 STRATIFIED SAMPLING [Seite 164]
9.6 - 5.6 MULTILEVEL MONTE CARLO [Seite 166]
9.7 - 5.7 IMPORTANCE SAMPLING [Seite 169]
9.7.1 - 5.7.1 Weighted Samples [Seite 169]
9.7.2 - 5.7.2 Variance Minimization Method [Seite 170]
9.7.3 - 5.7.3 Cross-Entropy Method [Seite 174]
9.8 - 5.8 SEQUENTIAL IMPORTANCE SAMPLING [Seite 179]
9.9 - 5.9 SEQUENTIAL IMPORTANCE RESAMPLING [Seite 185]
9.10 - 5.10 NONLINEAR FILTERING FOR HIDDEN MARKOV MODELS [Seite 187]
9.11 - 5.11 TRANSFORM LIKELIHOOD RATIO METHOD [Seite 191]
9.12 - 5.12 PREVENTING THE DEGENERACY OF IMPORTANCE SAMPLING [Seite 194]
9.13 - PROBLEMS [Seite 199]
9.14 - REFERENCES [Seite 204]
10 - CHAPTER 6 MARKOV CHAIN MONTE CARLO [Seite 207]
10.1 - 6.1 INTRODUCTION [Seite 207]
10.2 - 6.2 METROPOLIS-HASTINGS ALGORITHM [Seite 208]
10.3 - 6.3 HIT-AND-RUN SAMPLER [Seite 213]
10.4 - 6.4 GIBBS SAMPLER [Seite 214]
10.5 - 6.5 ISING AND POTTS MODELS [Seite 217]
10.5.1 - 6.5.1 Ising Model [Seite 217]
10.5.2 - 6.5.2 Potts Model [Seite 218]
10.6 - 6.6 BAYESIAN STATISTICS [Seite 220]
10.7 - 6.7 OTHER MARKOV SAMPLERS [Seite 222]
10.7.1 - 6.7.1 Slice Sampler [Seite 224]
10.7.2 - 6.7.2 Reversible Jump Sampler [Seite 225]
10.8 - 6.8 SIMULATED ANNEALING [Seite 228]
10.9 - 6.9 PERFECT SAMPLING [Seite 232]
10.10 - PROBLEMS [Seite 234]
10.11 - REFERENCES [Seite 239]
11 - CHAPTER 7 SENSITIVITY ANALYSIS AND MONTE CARLO OPTIMIZATION [Seite 241]
11.1 - 7.1 INTRODUCTION [Seite 241]
11.2 - 7.2 SCORE FUNCTION METHOD FOR SENSITIVITY ANALYSIS OF DESS [Seite 244]
11.3 - 7.3 SIMULATION-BASED OPTIMIZATION OF DESS [Seite 251]
11.3.1 - 7.3.1 Stochastic Approximation [Seite 252]
11.3.2 - 7.3.2 Stochastic Counterpart Method [Seite 257]
11.4 - 7.4 SENSITIVITY ANALYSIS OF DEDS [Seite 266]
11.5 - PROBLEMS [Seite 272]
11.6 - REFERENCES [Seite 275]
12 - CHAPTER 8 CROSS-ENTROPY METHOD [Seite 277]
12.1 - 8.1 INTRODUCTION [Seite 277]
12.2 - 8.2 ESTIMATION OF RARE-EVENT PROBABILITIES [Seite 278]
12.2.1 - 8.2.1 Root-Finding Problem [Seite 287]
12.2.2 - 8.2.2 Screening Method for Rare Events [Seite 288]
12.2.3 - 8.2.3 CE Method Combined with Sampling from the Zero-Variance Distribution [Seite 291]
12.3 - 8.3 CE METHOD FOR OPTIMIZATION [Seite 292]
12.4 - 8.4 MAX-CUT PROBLEM [Seite 296]
12.5 - 8.5 PARTITION PROBLEM [Seite 302]
12.5.1 - 8.5.1 Empirical Computational Complexity [Seite 303]
12.6 - 8.6 TRAVELING SALESMAN PROBLEM [Seite 303]
12.6.1 - 8.6.1 Incomplete Graphs [Seite 308]
12.6.2 - 8.6.2 Node Placement [Seite 309]
12.6.3 - 8.6.3 Case Studies [Seite 310]
12.7 - 8.7 CONTINUOUS OPTIMIZATION [Seite 311]
12.8 - 8.8 NOISY OPTIMIZATION [Seite 312]
12.9 - 8.9 MINXENT METHOD [Seite 314]
12.10 - PROBLEMS [Seite 318]
12.11 - REFERENCES [Seite 323]
13 - CHAPTER 9 SPLITTING METHOD [Seite 327]
13.1 - 9.1 INTRODUCTION [Seite 327]
13.2 - 9.2 COUNTING SELF-AVOIDING WALKS VIA SPLITTING [Seite 328]
13.3 - 9.3 SPLITTING WITH A FIXED SPLITTING FACTOR [Seite 330]
13.4 - 9.4 SPLITTING WITH A FIXED EFFORT [Seite 333]
13.5 - 9.5 GENERALIZED SPLITTING [Seite 334]
13.6 - 9.6 ADAPTIVE SPLITTING [Seite 338]
13.7 - 9.7 APPLICATION OF SPLITTING TO NETWORK RELIABILITY [Seite 341]
13.8 - 9.8 APPLICATIONS TO COUNTING [Seite 342]
13.9 - 9.9 CASE STUDIES FOR COUNTING WITH SPLITTING [Seite 345]
13.9.1 - 9.9.1 Satisfiability (SAT) Problem [Seite 345]
13.9.2 - 9.9.2 Independent Sets [Seite 350]
13.9.3 - 9.9.3 Permanent and Counting Perfect Matchings [Seite 352]
13.9.4 - 9.9.4 Binary Contingency Tables [Seite 354]
13.9.5 - 9.9.5 Vertex Coloring [Seite 356]
13.10 - 9.10 SPLITTING AS A SAMPLING METHOD [Seite 357]
13.11 - 9.11 SPLITTING FOR OPTIMIZATION [Seite 360]
13.11.1 - 9.11.1 Continuous Optimization [Seite 363]
13.12 - PROBLEMS [Seite 364]
13.13 - REFERENCES [Seite 368]
14 - CHAPTER 10 STOCHASTIC ENUMERATION METHOD [Seite 371]
14.1 - 10.1 INTRODUCTION [Seite 371]
14.2 - 10.2 TREE SEARCH AND TREE COUNTING [Seite 372]
14.3 - 10.3 KNUTH'S ALGORITHM FOR ESTIMATING THE COST OF A TREE [Seite 375]
14.4 - 10.4 STOCHASTIC ENUMERATION [Seite 377]
14.4.1 - 10.4.1 Combining SE with Oracles [Seite 379]
14.5 - 10.5 APPLICATION OF SE TO COUNTING [Seite 380]
14.5.1 - 10.5.1 Counting the Number of Paths in a Network [Seite 380]
14.5.2 - 10.5.2 Counting SATs [Seite 383]
14.5.3 - 10.5.3 Counting the Number of Perfect Matchings in a Bipartite Graph [Seite 386]
14.6 - 10.6 APPLICATION OF SE TO NETWORK RELIABILITY [Seite 388]
14.6.1 - 10.6.1 Numerical Results [Seite 390]
14.7 - PROBLEMS [Seite 393]
14.8 - REFERENCES [Seite 395]
15 - APPENDIX [Seite 397]
15.1 - A.1 CHOLESKY SQUARE ROOT METHOD [Seite 397]
15.2 - A.2 EXACT SAMPLING FROM A CONDITIONAL BERNOULLI DISTRIBUTION [Seite 398]
15.3 - A.3 EXPONENTIAL FAMILIES [Seite 399]
15.4 - A.4 SENSITIVITY ANALYSIS [Seite 402]
15.4.1 - A.4.1 Convexity Results [Seite 403]
15.4.2 - A.4.2 Monotonicity Results [Seite 404]
15.5 - A.5 A SIMPLE CE ALGORITHM FOR OPTIMIZING THE PEAKS FUNCTION [Seite 405]
15.6 - A.6 DISCRETE-TIME KALMAN FILTER [Seite 405]
15.7 - A.7 BERNOULLI DISRUPTION PROBLEM [Seite 407]
15.8 - A.8 COMPLEXITY [Seite 409]
15.8.1 - A.8.1 Complexity of Rare-Event Algorithms [Seite 409]
15.8.2 - A.8.2 Complexity of Randomized Algorithms: FPRAS and FPAUS [Seite 410]
15.8.3 - A.8.3 SATs in CNF [Seite 414]
15.8.4 - A.8.4 Complexity of Stochastic Programming Problems [Seite 415]
15.9 - PROBLEMS [Seite 422]
15.10 - REFERENCES [Seite 423]
16 - ABBREVIATIONS AND ACRONYMS [Seite 425]
17 - LIST OF SYMBOLS [Seite 427]
18 - INDEX [Seite 429]
19 - EULA [Seite 435]

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