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Bayesian Statistics
Siliang Zhang (slzhang at ecnu dot edu dot cn)
Spring 2024, 2025
Course Information:
Target: Statistics Major Students
Course Website: Bayesian Statistics
课程简介 Course Description
《贝叶斯统计学》是为统计学及相关专业的学生开设的课程。在学习完课程中的讲义后，要求学生掌握贝叶斯推断中的基本建模方法，包括单参数和和多参数模型在内的常用模型，以及贝叶斯计算方法，如马尔科夫链蒙特卡洛算法。本课程将在R编程语言的帮助下进行教学。JAGS和一些著名的贝叶斯推断的R软件包，如LearnBayes, R2OpenBUGS, rjags, nimble等将被讲授并用于案例研究。学习本课程要求学生应该有一些基础统计知识和R编程技能。
Bayesian Statistics is a course for students majoring in statistics. After learning the lectures in the course, the students are required to get a good command of basic modeling methods in Bayesian inference, common models including one-parameter and multi-parameter models, and Bayesian computation methods such as Markov chain Monte Carlo algorithms. This course will be taught with the help of the R programming language. WinBUGS/OpenBUGS and some well-known R packages for Bayesian inference, such as LearnBayes, R2OpenBUGS, rjags, nimble, etc. will be taught and used for case studies. Students should have some knowledge of basic statistics and R programming skills.
课程目标 Course Objectives
本课程旨在培养学生运用贝叶斯分析方法数据分析的能力，要求学生：
1. 掌握贝叶斯统计分析中的基本概念、基本理论和计算方法 2. 学会具体数据的贝叶斯建模与分析方法 3. 掌握贝叶斯统计分析的专业词语和表达方法，看懂一些简单的参考文献 4. 学会通过R编程和BUGS及相关包进行贝叶斯统计分析
教材 Textbooks
Applied Bayesian Statistics: with R and OpenBUGS Examples by M. K. Cowles, Springer, 2013
Bayesian Computation with R (2nd Edition) by J. Albert, Springer, 2009
参考书目 Reference Books
Doing Bayesian Data Analysis: A Tutorial with R and BUGS by J. K. Kruschke, Academic Press/Elsevier, 2011
R in Action: Data Analysis and Graphics with R by Robert Kabacoff, Manning Publications, 2011
课程内容 Course Content
| Chapter | Topic (English) | Topic (中文) | Week |
| Chapter 1 | What is Bayesian Statistics? | 什么是贝叶斯统计? | 1 |
| Chapter 2 | Introduction to R for Bayesian Analysis | 针对贝叶斯分析的R介绍 | 1-2 |
| Chapter 3 | Introduction to One-parameter Models: Estimating a Population Proportion | 单参数模型介绍: 估计总体的比例 | 2-3 |
| Chapter 4 | Bayesian Inference for a Population Proportion | 总体比例的贝叶斯推断 | 3-4 |
| Chapter 5 | Special Considerations in Bayesian Inference | 贝叶斯推断中的特殊考虑因素 | 4-5 |
| Chapter 6 | Other One-Parameter Models and Their Conjugate Priors | 其他单参数模型及共轭先验 | 5-6 |
| Chapter 7 | Introduction to Multiparameter Models | 多参数模型介绍 | 6-7 |
| Chapter 8 | Fitting More Complex Bayesian Models: Markov Chain Monte Carlo | 贝叶斯计算拟合更复杂的贝叶斯模型: 马氏链蒙特卡罗方法 | 7-8 |
| Chapter 9 | Bayesian Inference based on BUGS Engines | 基于BUGS引擎进行贝叶斯推断 | 8-9 |
| Chapter 10 | Hierarchical Models and More on Convergence Assessment | 分层模型及更多收敛性评估 | 9-10 |
| Chapter 11 | Regression and Hierarchical Regression Models | 回归与分层回归模型 | 10-11 |