R Programming for Simulation and Monte Carlo Methods

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**课程名称:** R语言在模拟与蒙特卡洛方法中的应用 **课程概述:** 本课程专注于利用R语言进行概率模拟,也被称为蒙特卡洛模拟。课程将通过生动有趣的“真实世界”案例,如模拟棒球选手连续20场比赛的“安打”概率,或是在特定时间内观察到一系列编号出租车经过街角,来估计未知城市中出租车的总数。 课程不仅会详细介绍这些应用案例,还会深入讲解如何使用现有的R函数以及如何编写自定义R函数,以执行模拟推断估计,包括似然度、置信区间和其他随机模拟。 此外,课程还将详细阐述如何利用R生成各种随机变量族的特性,并教授实现各种方法的技能,包括: * 模拟连续和离散随机变量的概率分布函数 * 参数估计 * 蒙特卡洛积分 * 方​​差缩减技术 课程还将部分利用R的CRAN(Comprehensive R Archive Network)上的spuRs包,展示如何构建和编写程序,以使用R统计软件完成数学和概率模拟。

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R Programming for Simulation and Monte Carlo Methods focuses on using R software to program probabilistic simulations, often called Monte Carlo Simulations. Typical simplified "real-world" examples include simulating the probabilities of a baseball player having a 'streak' of twenty sequential season games with 'hits-at-bat' or estimating the likely total number of taxicabs in a strange city when one observes a certain sequence of numbered cabs pass a particular street corner over a 60 minute period. In addition to detailing half a dozen (sometimes amusing) 'real-world' extended example applications, the course also explains in detail how to use existing R functions, and how to write your own R functions, to perform simulated inference estimates, including likelihoods and confidence intervals, and other cases of stochastic simulation. Techniques to use R to generate different characteristics of various families of random variables are explained in detail. The course teaches skills to implement various approaches to simulate continuous and discrete random variable probability distribution functions, parameter estimation, Monte-Carlo Integration, and variance reduction techniques. The course partially utilizes the Comprehensive R Archive Network (CRAN) spuRs package to demonstrate how to structure and write programs to accomplish mathematical and probabilistic simulations using R statistical software.

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