课程号:00137960
课程名称:统计思维
开课学期:春
学分: 3
先修课程:微积分、线性代数
基本目的:该课程提供一个较为系统、基础、前沿性的统计学概论,课程主要包含:统计学原理、统计推理、贝叶斯推理、统计模型和方法等。帮助学生学会如何实现或应用统计学方法和模型,并能掌握统计学所蕴含的数学机理,从而培养学生的统计分析与思维能力。
内容提要:
1 Basic Concepts and Applications
1)Likelihood 2)Sufficiency 3)Exponential family 4)Frequentist 5)Minimax theory
2 Interpretations of Uncertainty
3 Statistical Inference
1)Inference, learning and information 2)parametric and nonparametric methods
3)The Bootstrap 4)Hypothesis testing and p-values
4 Bayesian Inference
1)The Bayesian paradigm 2)Parametric models 3)Statistical decision theory
5 Statistical Models and Methods
1)Linear models 2)Generalized linear models 3)Generalized additive models
4)Random effect modes 5)Robust estimation 6)Online learning
6 Nonparametric Statistics
1)The bootstrap and the jackknife 2)Nonparametric regression 3)Density estimation
7 Advantaged Topics
1)Design and analysis of experiments 2)A/B test 3)Empirical Bayes
4)False discovery rate 5)Large-scale hypothesis testing
教学方式:课堂讲授,每周3学时
教材与参考书:
1. Cox, D. R.(2006).Principles of Statistical Inference.Cambridge University Press.
2. Efron, B. and Hastie, T. (2016). Computer Age Statistical Inference: Algorithms, Evidence, and Data Science. Cambridge University Press.
3. Rao, C. R. (1997). Statistics and Truth: Putting Chance to Work (2nd ed.). World Scientific.
4. Stigler, S. M. (2016). The Seven Pillars of Statistical Wisdom. Harvard University Press.
学生成绩评定方法:平时作业50%,期末论文50%。
课程修订负责人:张志华 林伟