统计模拟入门:R语言实现的蒙特卡洛方法

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"《Introducing Monte Carlo Methods with R》是一本详细介绍统计模拟中主要工具的书籍,特别是从程序员的角度出发,讲解如何用R语言实现各种蒙特卡洛模拟技术,并提供输出结果以便理解和比较。书中涵盖了从基础的R编程到复杂的马尔科夫链蒙特卡洛(MCMC)算法的多个主题。" 该书由Christian P. Robert和George Casella合著,他们是统计学领域的专家,分别来自法国巴黎大学和美国佛罗里达大学。该书的顾问包括知名统计学家Robert Gentleman、Kurt Hornik和Giovanni Parmigiani,他们都是在R编程和统计模拟领域有着深厚造诣的学者。 书中内容结构如下: 1. **基本R编程**:这一章为读者提供了R语言的基础知识,这是进行蒙特卡洛模拟工作的必备技能,包括数据类型、操作符、控制流以及函数的使用等。 2. **随机变量生成**:介绍了如何在R中生成各种概率分布的随机变量,如均匀分布、正态分布、二项分布等,这是蒙特卡洛方法的核心部分。 3. **蒙特卡洛积分**:通过大量的随机抽样来近似复杂函数的积分,这是蒙特卡洛方法的基本应用之一。 4. **控制和加速收敛**:讨论如何提高模拟效率,包括重要性采样、变分法等技术,以加速蒙特卡洛方法的收敛速度。 5. **蒙特卡洛优化**:利用随机搜索策略进行参数估计和最优化问题的解决。 6. **Metropolis-Hastings算法**:这是一种广泛使用的MCMC算法,用于在高维空间中探索概率分布。 7. **Gibbs采样器**:Gibbs采样是MCMC的一种特殊形式,可以处理多变量的概率模型。 8. **MCMC算法的收敛监控与适应**:讲述了如何监测和调整算法的运行,确保其正确性和效率,例如使用 Geweke 统计量和 autocorrelation 分析。 该书的出版旨在帮助读者深入理解蒙特卡洛方法,并提供实际操作的指导,适合统计学、数据科学、计算生物学等领域对模拟技术感兴趣的读者。此外,书中包含的实际代码输出将有助于读者直观地理解理论概念,从而更好地将理论应用于实践。通过阅读本书,读者不仅可以掌握R语言的模拟技巧,还能了解如何利用蒙特卡洛方法解决实际问题。
2012-08-22 上传
Computational techniques based on simulation have now become an essential part of the statistician's toolbox. It is thus crucial to provide statisticians with a practical understanding of those methods, and there is no better way to develop intuition and skills for simulation than to use simulation to solve statistical problems. Introducing Monte Carlo Methods with R covers the main tools used in statistical simulation from a programmer's point of view, explaining the R implementation of each simulation technique and providing the output for better understanding and comparison. While this book constitutes a comprehensive treatment of simulation methods, the theoretical justification of those methods has been considerably reduced, compared with Robert and Casella (2004). Similarly, the more exploratory and less stable solutions are not covered here. This book does not require a preliminary exposure to the R programming language or to Monte Carlo methods, nor an advanced mathematical background. While many examples are set within a Bayesian framework, advanced expertise in Bayesian statistics is not required. The book covers basic random generation algorithms, Monte Carlo techniques for integration and optimization, convergence diagnoses, Markov chain Monte Carlo methods, including Metropolis {Hastings and Gibbs algorithms, and adaptive algorithms. All chapters include exercises and all R programs are available as an R package called mcsm. The book appeals to anyone with a practical interest in simulation methods but no previous exposure. It is meant to be useful for students and practitioners in areas such as statistics, signal processing, communications engineering, control theory, econometrics, finance and more. The programming parts are introduced progressively to be accessible to any reader.