Handbook of Monte Carlo Methods

Dirk P. Kroese, Thomas Taimre, Zdravko I. Botev

• Publisher: Wiley
• Year: 2013
• Print ISBN: 9780470177938
• eBook ISBN: 9781118014950
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

A comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications

More and more of today's numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field.

The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including:

• Random variable and stochastic process generation
• Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run
• Discrete-event simulation
• Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation
• Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo
• Estimation of derivatives and sensitivity analysis
• Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization

The presented theoretical concepts are illustrated with worked examples that use MATLAB®, a related Web site houses the MATLAB® code, allowing readers to work hands-on with the material and also features the author's own lecture notes on Monte Carlo methods. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation.

Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research. It is also a suitable supplement for courses on Monte Carlo methods and computational statistics at the upper-undergraduate and graduate levels.

Table of contents

• Cover
• Contents
• Title page
• Copyright
• Dedication
• Preface
• Acknowledgments
• CHAPTER 1: Uniform Random Number Generation
• CHAPTER 2: Quasirandom Number Generation
• CHAPTER 3: Random Variable Generation
• CHAPTER 4: Probability Distributions
• CHAPTER 5: Random Process Generation
• CHAPTER 6: Markov Chain Monte Carlo
• CHAPTER 7: Discrete Event Simulation
• CHAPTER 8: Statistical Analysis of Simulation Data
• CHAPTER 9: Variance Reduction
• CHAPTER 10: Rare-Event Simulation
• CHAPTER 11: Estimation of Derivatives
• CHAPTER 12: Randomized Optimization
• CHAPTER 13: Cross-Entropy Method
• CHAPTER 14: Particle Methods
• CHAPTER 15: Applications to Finance
• CHAPTER 16: Applications to Network Reliability
• CHAPTER 17: Applications to Differential Equations
• Appendix A: Probability and Stochastic Processes
• Appendix B: Elements of Mathematical Statistics
• Appendix C: Optimization
• Appendix D: Miscellany
• Acronyms and Abbreviations
• List of Symbols
• List of Distributions
• Index