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. INDICE: Table of Contents .Dedication .Preface .Acknowledgments .Chapter 1: Preliminaries .1.1 Introduction .1.2 Random Experiments .1.3 Conditional Probability and Independence .1.4 Random Variables and Probability Distributions .1.5 Some Important Distributions .1.6 Expectation .1.7 Joint Distributions .1.8 Functions of Random Variables .1.9 Transforms .1.10 Jointly Normal Random Variables .1.11 Limit Theorems .1.12 Poisson Processes .1.13 Markov Processes .1.14 Gaussian Processes .1.15 Information .1.16 Convex Optimization and Duality Problems .References .Chapter 2: Random Number, Random Variable, and Stochastic Process Generation .2.1 Introduction .2.2 Random Number Generation .2.3 Random Variable Generation .2.4 Generating from Commonly Used Distributions .2.5 Random Vector Generation .2.6 Generating Poisson Processes .2.7 Generating Markov Chains and Markov Jump Processes .2.8 Generating Gaussian Processes .2.9 Generating Diffusion Processes .2.10 Generating Random Permutations .Problems .References .Chapter 3: Simulation of Discrete–Event Systems .3.1 Introduction .3.2 Simulation Models .3.3 Simulation Clock and Event List for DEDS .3.4 Discrete–Event Simulation Problems .References .Chapter 4: Statistical Analysis of Discrete–Event Systems .4.1 Introduction .4.2 Estimators and Confidence Intervals .4.3 Static Simulation Models .4.4 Dynamic Simulation Models .4.5 The Bootstrap Method .Problems .References .Chapter 5: Controlling the Variance .5.1 Introduction .5.2 Common and Antithetic Random Variables .5.3 Control Variables .5.4 Conditional Monte Carlo .5.5 Stratified Sampling .5.6 Multilevel Monte Carlo .5.7 Importance Sampling .5.8 Sequential Importance Sampling .5.9 Sequential Importance Resampling .5.10 Nonlinear Filtering for Hidden Markov Models .5.11 The Transform Likelihood Ratio Method .5.12 Preventing the Degeneracy of Importance Sampling .Problems .References .Chapter 6: Markov Chain Monte Carlo .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 .6.6 Bayesian Statistics .6.7 Other Markov Samplers .6.8 Simulated Annealing .6.9 Perfect Sampling .Problems .References .Chapter 7: Sensitivity Analysis and Monte Carlo Optimization .7.1 Introduction .7.2 The Score Function Method for Sensitivity Analysis of DESS .7.3 Simulation–Based Optimization of DESS .7.4 Sensitivity Analysis of DEDS .Problems .References .Chapter 8: Cross–Entropy Method .8.1 Introduction .8.2 Estimation of Rare–Event Probabilities .8.3 The CE Method for Optimization .8.4 The Max–cut Problem .8.5 The Partition Problem .8.6 The Traveling Salesman Problem .8.7 Continuous Optimization .8.8 Noisy Optimization .8.9 The MinxEnt Method .Problems .References .Chapter 9: Splitting Method .9.1 Introduction .9.2 Counting Self–Avoiding Walks via Splitting .9.3 Splitting with a Fixed Splitting Factor .9.4 Splitting with a Fixed Effort .9.5 Generalized Splitting .9.6 Adaptive Splitting .9.7 Application of Splitting to Network Reliability .9.8 Applications to Counting .9.9 Case Studies for Counting with Splitting .9.10 Splitting as a Sampling Method .9.11 Splitting for Optimization .Problems .References .Chapter 10: Stochastic Enumeration Method .10.1 Introduction .10.2 Tree Search and Tree Counting .10.3 Knuth?s Algorithm for Estimating the Cost of a Tree .10.4 Stochastic Enumeration .10.5 Application of SE to Counting .10.6 Application of SE to Network Reliability .Problems .References .Appendix .A.1 Cholesky Square Root Method .A.2 Exact Sampling from a Conditional Bernoulli Distribution .A.3 Exponential Families .A.4 Sensitivity Analysis .A.5 A Simple CE Algorithm for Optimizing the Peaks Function .A.6 Discrete–time Kalman Filter .A.7 Bernoulli Disruption Problem .A.8 Complexity .Problems .References .Abbreviations and Acronyms .List of Symbols .Index
- ISBN: 978-1-118-63216-1
- Editorial: Wiley–Blackwell
- Encuadernacion: Cartoné
- Páginas: 432
- Fecha Publicación: 02/12/2016
- Nº Volúmenes: 1
- Idioma: Inglés