研究生课程《数据分析与统计计算》教学大纲

1、研究生课程数据分析与统计计算教学大纲研究生课程教学大纲课程编号：Math2103课程名称：数据分析与统计计算英文名称：Data Analysis and Computational Statistics Methods开课单位：安大数学科学学院开课学期：秋课内学时：36教学方式：英文讲授适用专业及层次：统计学专业与计算数学专业硕士生考核方式：考试预修课程：概率论与数理统计、线性代数一、教学目标与要求This course aims to prepare students to input, verify, organise, modify, combine, analyse and prese

2、nt data using a range of computing and statistical methods implemented in thegeneral purpose statistical packages. Topics include generation of random numbers,Monte Carlo methods, optimization methods, numerical integration, resampling methods such as the Bootstrap and the Jackknife, and advanced Ba

3、yesian computational tools such as the Gibbs sampler, Metropolis Hastings, the method of auxiliary variables, marginal and conditional data augmentation, slice sampling, exact sampling, and reversible jump MCMC. Computer programming exercises apply the methods discussed in class二、课程内容与学时分配 Chapter 1

4、 Preface Chapter2 Turning Data Into Information（4课时） Raw Data Types of Data Summarizing One or Two Categorical variables Finding Information in Quantitative Data Pictures for Quantitative Data Numerical Summaries of Quantitative Variables Bell-Shaped Distributions of Number Chapter 3 Gathering Usefu

5、l Data（4课时） Description or Decision? using Data Wisely Speaking the Language of Research Studies Designing a Good Experiment Designing a Good Observation Difficulties and Disasters in Experiments and Observational Studies Chapter 4 sampling（4课时） The beauty of Sampling Simple Random Sampling and Rand

6、omization Other Sampling Methods Difficulties and Disasters in Sampling How to Ask Survey Questions Chapter 5 Relationships Between Quantitative Variables（4课时） Looking for Patterns with Scatterplots Describing Linear Patterns with a Regression Line Measuring Strength and Direction with Correlation W

7、hy the Answers May Not Make Sense Correlation Does Not Prove Causation Chapter 6 Relationships Between Categorical Variables（4课时） Displaying relationships between Categorical Variables Risk, Relative Risk, Odds Ratio, and Increased Risk Misleading Statistics About Risk The Effect of a Third Variable

8、 and Simpsons Paradox Assessing the Statistical Significance of a 2*2 Table Chapter 7 Computational Statistics Experiments designing Topic 1: Generation of random numbers,（2课时） Topic 2: Monte Carlo methods, optimization methods,（2课时） Topic 3: Numerical integration, resampling methods such as the Boo

9、tstrap and the Jackknife,（2课时） Topic 4: Advanced Bayesian computational tools such as the Gibbs sampler（2 课时）, Metropolis Hastings（2课时）, the method of auxiliary variables（2课 时）, marginal and conditional data augmentation, slice sampling（2课时）, exact sampling, and reversible jump MCMC（2课时）四、教材Springer Handbook of Computational Statistics Concepts and MethodsEditors: Gentle, James E., Hrdle, Wolfgang Karl, Mori, Yuichi (Eds.)主要参考书1J. A. Rice, Mathematical Statistics and Data Analysis, 2nd edition, Duxbury