Description
Presents detailed guidance on Monte Carlo integration methods for complex applications
Monte Carlo integration has become an indispensable computational tool across science, engineering, mathematics, and economics, offering effective solutions where traditional numerical integration methods fall short. Monte Carlo Integration with MATLAB and Simulink provides both a structured introduction to advanced integration techniques and a practical guide to applying them in real-world contexts. Author Arthur A. Giordano emphasizes the natural progression from traditional methods such as the use of MATLAB integral to Monte Carlo simulation-based approaches, highlighting the growing importance of random variable–driven computations in modern research and engineering applications.
Covering topics from accept-rejection sampling and importance sampling to advanced algorithms such as Metropolis-Hastings, Gibbs Sampling, Slice, Hamiltonian Monte Carlo, and Sequential Monte Carlo (Particle Filtering), the book equips readers with the knowledge to handle both tractable and intractable integration problems. Extensive MATLAB examples are paired with detailed explanations, while dedicated Simulink models extend the scope of applications to robotics, control systems, neural networks, cosmology, and more. By integrating step-by-step examples, code snippets, and exploratory exercises, the book fosters an interactive learning process that encourages readers to replicate, modify, and expand on the provided material.
Combining theoretical background with extensive computational demonstrations, Monte Carlo Integration with MATLAB and Simulink:
- Covers both deterministic and simulation-based integration methods with increasing depth and complexity
- Introduces advanced Monte Carlo sampling algorithms, including Gibbs Sampling and Sequential Monte Carlo (Particle Filtering)
- Features over a dozen fully developed MATLAB examples with accompanying program code
- Provides detailed Simulink models for robotics, control systems, and scientific applications
- Includes problem sets with solutions available on a companion website
- Highlights the transition from classical integration to simulation methods for random processes
Incorporating classical integration techniques and cutting-edge simulation methods, Monte Carlo Integration with MATLAB and Simulink is a valuable resource for advanced undergraduate and graduate students in applied mathematics, engineering, and computational sciences, as well as scientists, engineers, and researchers applying Monte Carlo integration in fields ranging from signal processing to robotics.
Table of Contents
Preface xiii
Acknowledgments xxi
About the Software xxiii
Abbreviations and Acronyms xxv
List of MATLAB and Simulink Programs xxvii
About the Companion Website xxxi
1 Monte Carlo and Numerical Integration Methods 1
2 Numerical Integration 3
3 MATLAB Integral Programs 11
4 Monte Carlo Integration 21
5 Monte Carlo Integration: A Binary Choice 39
6 Monte Carlo Integration of a Normal Probability Density Function 57
7 Integration Using Importance Sampling 81
8 Further Methods of Monte Carlo Sampling 97
9 Metropolis–Hastings (MH) and Markov Chain Monte Carlo (MCMC) 125
10 Gibbs Sampling 179
11 Slice Sampling 207
12 Hamiltonian Monte Carlo Sampling 219
13 Sequential Monte Carlo or Particle Filtering 237
14 Numerical Integration via Simulink 257
15 Summary of Monte Carlo Integration Methods 309
Index 343
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- 電子書籍
- 月刊 クーヨン 2026年5月号
