Simulation and the Monte Carlo Method

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John Wiley & Sons, Sep 20, 2011 - Mathematics - 372 pages
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This accessible new edition explores the major topics in MonteCarlo simulation

Simulation and the Monte Carlo Method, Second Editionreflects the latest developments in the field and presents a fullyupdated and comprehensive account of the major topics that haveemerged in Monte Carlo simulation since the publication of theclassic First Edition over twenty-five years ago. Whilemaintaining its accessible and intuitive approach, this revisededition features a wealth of up-to-date information thatfacilitates a deeper understanding of problem solving across a widearray of subject areas, such as engineering, statistics, computerscience, mathematics, and the physical and life sciences.

The book begins with a modernized introduction that addressesthe basic concepts of probability, Markov processes, and convexoptimization. Subsequent chapters discuss the dramatic changes thathave occurred in the field of the Monte Carlo method, with coverageof many modern topics including:

  • Markov Chain Monte Carlo
  • Variance reduction techniques such as the transform likelihoodratio method and the screening method
  • The score function method for sensitivity analysis
  • The stochastic approximation method and the stochasticcounter-part method for Monte Carlo optimization
  • The cross-entropy method to rare events estimation andcombinatorial optimization
  • Application of Monte Carlo techniques for counting problems,with an emphasis on the parametric minimum cross-entropymethod

An extensive range of exercises is provided at the end of eachchapter, with more difficult sections and exercises markedaccordingly for advanced readers. A generous sampling of appliedexamples is positioned throughout the book, emphasizing variousareas of application, and a detailed appendix presents anintroduction to exponential families, a discussion of thecomputational complexity of stochastic programming problems, andsample MATLAB programs.

Requiring only a basic, introductory knowledge of probabilityand statistics, Simulation and the Monte Carlo Method,Second Edition is an excellent text for upper-undergraduate andbeginning graduate courses in simulation and Monte Carlotechniques. The book also serves as a valuable reference forprofessionals who would like to achieve a more formal understandingof the Monte Carlo method.

 

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Contents

Preface
Random Number Random Variable
Problems
Simulation of DiscreteEvent Systems
Counting viaMonte Carlo
Markov ChainMonte Carlo
Statistical Analysisof DiscreteEvent Systems 4 1 Introduction 4 2 Static Simulation Models
Controlling theVariance
Problems
Sensitivity Analysisand MonteCarlo Optimization
The CrossEntropy Method
and Decision Making 9 7 Numerical Results
Appendix
Sensitivity Analysis
Abbreviations and Acronyms
Index

Sampling

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About the author (2011)

Reuven Y. Rubinstein, DSc, is Professor Emeritus in theFaculty of Industrial Engineering and Management at Technion-IsraelInstitute of Technology. He has served as a consultant at numerouslarge-scale organizations, such as IBM, Motorola, and NEC. Theauthor of over 100 articles and six books, Dr. Rubinstein is alsothe inventor of the popular score-function method in simulationanalysis and generic cross-entropy methods for combinatorialoptimization and counting.

Dirk P. Kroese, PhD, is Senior Lecturer in Statistics inthe Department of Mathematics at The University of Queensland,Australia. He has published over fifty articles in a wide range ofareas in applied probability and statistics, including Monte Carlomethods, cross-entropy, randomized algorithms, tele-traffic theory,reliability, computational statistics, applied probability, andstochastic modeling.

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