本课程采用易于处理的生活中的许多实例作为例子，主要介绍随机模拟建模的基本方法：包括由输入、输出、分析和实验设计及编程方法组成的五步建模法。介绍马尔可夫链的蒙特卡洛法；Metropolis算法及其推广；随机数生成法；以及大量实际复杂问题中的模拟典型案例，同时如果学生没有用计算机编程的算法经验，我们介绍配套的Matlab编程语言。我们的目标是给学生对感兴趣或重要的复杂类问题的各种领域用简洁、准确、综合的模拟方法的设计留下更多的创新空间。
This course is a simple and complex science. It is a system that is a mathematical or logical model actual decision-making problems, and to test the model in order to gain understanding of the system behavior or process to solve practical problems. Although the course uses tractable stochastic process models (e.g., Markovian queues) as examples, students may find the stochastic processes course more intuitive and meaningful after having worked through this course. The contents include introduction to Monte Carlo methods; Markov Chain Monte Carlo; the metropolis algorithm and the ergodic theorem; optimization by Monte Carlo methods; random walks and generating random numbers. Programming (eg MATLAB) is at the heart of stochastic simulation methods and will be the primary activity of our work in this course. The hope is that an instructor will want students to read all of the course to get a complete, coherent picture before jumping off into other reference texts or journal papers.
课程教学大纲（course syllabus） |
*学习目标(Learning Outcomes) | 1．针对大量用经典的严密的数学方法难以求解的实际问题和数学难题，学会数学建模并运用随机模拟方法，解决处理实际问题。 2．学会随机模拟中一般理论、建模方法和MCMC方法。 3．学会MATLAB计算机编程语言。 4．通过阅读完成大作业，学会初步撰写论文的能力。为理工科各专业学生进一步开创性研究打下基础。 （1. This course is a fundamental course in Stochastic Modeling and Methods of Stochastic Simulation.It provides the basic knowledge for students to research Stochastic Modeling and methods of Stochastic Simulation problems. 2. On studying the general theories and research methods of Monte-Carlo and System simulation, at the same time by the developmental experiment, it can cultivate the basic technology of students, who will be engaged in the research and application fields of all different kinds of engineering and research. 3. Learn MATLAB computer language. At once students are required to catch corresponding algorithms and theories and to be capable of programming as well. 4. By reading and completed Paper, it can cultivate the basic technology of students, who will be engaged in the research and application fields of all different kinds of engineering and research. |
*教学内容、进度安排及要求 (Class Schedule & Requirements) | 教学内容 | 学时 | 教学方式 | 作业及要求 | 基本要求 | 考查方式 | 第1章 课程简介：初识随机模拟方法什么是随机模拟？几个简单例子: 电池问题、蒙提霍尔问题、商品优惠券问题、蒲丰投针法求圆周率等等 (Introduction chapter first courses: first what is the stochastic simulation method of stochastic simulation? A few simple examples: the battery problem, Monty Holzer issue, commodity coupon issues, Buffon needle for PI and so on.） | 3 | 课堂 | EX1-1,EX1-2 | | | 第2章 懂点概率论：领会描述随机性的数学语言 直观的理解概率的公理定义及性质、随机变量与概率分布、随机变量的数字特征、随机变量的变换、大数定律等 (The second chapter understand the point of probability theory: grasp the mathematical description of the random nature of the language. Understanding probability of intuitive axiomatic definition and nature, random variables and probability distribution, numerical characteristics, random variables random variable transformation, the law of large numbers and CLT.) | 3 | 课堂 | EX2-1,EX2-2 | | | 第3章 善用身边的数学秘书：学会使用Matlab软件 MATLAB快速入门、MATLAB的作图功能、Matlab程序设计 (The third chapter use mathematical Secretary side: learn to use Matlab software.MATLAB quick start, MATLAB plot, Matlab program design) | 3 | 课堂 | EX3-1,EX3-2 | | | 第4章 让电脑玩掷骰子：使用Matlab生成随机数 离散型概率分布及其随机数的生成 连续型概率分布及其随机数的生成 (The fourth chapter make the computer play dice: use Matlab to generate random numbers.The generation of discrete /continuous probability distribution and random number.) | 3 | 课堂 | EX4-1,EX4-2 | | | 第5章 掷骰子的进阶：特殊分布随机数的抽样 逆变换法、接受-拒绝法、 (fifth chapter Advanced Dice: a random number of special distribution sampling.Inversion method, acceptance rejection method) | 3 | 课堂 | EX5-1,EX5-2 | | | 第5章 掷骰子的进阶：特殊分布随机数的抽样 抽样多维联合分布的方法 (Methods multidimensional joint distribution sampling) | 3 | | EX5-3,EX5-4 | | | 第6章 神奇的马尔科夫链蒙特卡罗方法 马尔可夫链、MCMC抽样―Metropolis算法、几个MCMC的例子 (The sixth chapter Markov Monte Carlo.Markov chain, MCMC sampling and Metropolis algorithm, several examples of MCMC) | 3 | | EX6-1,EX6-2 | | | 第6章 神奇的马尔科夫链蒙特卡罗方法应用：统计力学 为什么Metropolis算法能有效工作？ 统计力学、系综方法与玻尔兹曼分布、伊辛模型和Metropolis算法 (Why Metropolis algorithm can effectively work?Statistical mechanics, ensemble method and Boltzmann distribution, Ising model and Metropolis algorithm) | 3 | | | | | 第7章 仿真随机服务系统 随机服务系统的组成与特征、举例及模拟 (The seventh chapter the simulation of random service system.Examples and simulation, composition and characteristics of random service system) | 3 | | | | | 第8章 不落俗套：蒙特卡罗优化方法 模拟退火法、遗传算法 (The eighth chapter conform to no conventional pattern: Monte Carlo method. Simulated annealing, genetic algorithm) | 3 | | | | | 第9章 模拟醉汉行走：随机游走模型 布朗运动与扩散现象 随机游走的应用一：金融期权定价 (The ninth chapter simulation drunk walking: random walk model Brown motion and diffusion phenomenon. An application of financial option pricing: random walk) | 3 | | | | | 第9章 模拟醉汉行走：随机游走应用 随机游走应用二：金融的凯利判据、赌徒的破产 (The application of two random walk: gambler Kelly criterion, financial bankruptcy) | 3 | | | | | 第10 章化腐朽为神奇：蒙特卡洛积分法 求定积分的随机投点法、样本平均法、重要性抽样法 (The tenth chapter turn bad into good: Monte Carlo integration method. For the integral random methods, sample average method, importance sampling method) | 3 | | | | | 机动或大作业交流 Representation and discussion &Others | 3 | | | | | 随堂考试 | 3 | | | | |
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*考核方式 (Grading) | 期终卷面笔试40%+大作业40%+平时成绩20% The final test （40%）+ Report（40%）+ Performance（20%） |
*教材或参考资料 (Textbooks & Other Materials) | [1] 肖柳青 周石鹏，随机模拟方法与应用，北京大学出版社，2014.9
[2] Evolutionary Computation for Modeling and Optimization, Springer-Verlag, New York, 2006. [3 ] Hull, T.E.,Dobell, A.R., “Random Number Generators,” SIAM Review,4, 230–254, 1962.
[4] Bratley, P., Fox, B., and Scrage, L., A Guide to Simulation, Springer-Verlag, New York |
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