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基本説明
Most ideas are introduced and explained by way of concrete examples, algorithms, and practical experiments.
Full Description
This accessible new edition explores the major topics in Monte Carlo simulation Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years 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 the transform likelihood ratio method and the screening 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 to rare events estimation and combinatorial optimization
Application of Monte Carlo techniques for counting problems, with an emphasis on the parametric minimum cross-entropy method
An extensive range of exercises is provided at the end of each chapter, with more difficult sections and exercises marked accordingly for advanced readers. A generous sampling of applied examples is positioned throughout the book, emphasizing various areas of application, and a detailed appendix presents an introduction to exponential families, a discussion of the computational complexity of stochastic programming problems, and sample MATLAB® programs.
Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in 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.
Contents
Preface. Acknolwedgments.
I: Problems.
1. Preliminaries.
2. Random Number, random Variable, and Stochastic Process Generation.
3. Simulatin of Discrete-Event Systems.
4. Stastical Analysis of Discrete-Event Systems.
5. Controlling the Variance.
6. Markov Chain Monte Carlo.
7. Sensitivity Analysis and Monte Carlo Optimization.
8. The Cross-Entropy Method.
9. Counting via Monte Carlo.
10. Appendix.
II: Solutions.
11. Prelimiaries.
12. Random Number, Random Variable, and Stochastic Process Generation.
13. Simulatin of Discrete-Event Systems.
14. Stastical Analysis of Discrete-Event Systems.
15. Controlling the Variance.
16. Markov Chain Monte Carlo.
17. Sensitivity Analysis and Monte Carlo Optimization.
18. The Cross-Entropy Method.
19. Counting via Monte Carlo.
20. Appendix.
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