數理統計
Mathematical statistics
| 節 | 週二 |
|---|---|
3 10:10–11:00 | 數理統計 YL839 2 節連堂 |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
The course aims to introduce theory and applications in mathematical statistics. Topics include probability theory, sample theory, hypothesis testing, parameter estimation, regression, and non-parametric inference. A distinct feature of this course is the use of computer simulations to help the students understand abstract knowledge in statistics. Therefore, computer programming in MATLAB and R are heavily used to facilitate learning concepts and data analysis. Students are expected to develop solid understanding of statistical concepts and acquire data analysis skills (knowing how to code your own analysis). No programming experience is required. Some background in Calculus will help but not necessary. Since the course is required for entry-level cognitive neuroscience graduate students, some data and examples are from research related to brain and behavior.
| 週次 | 主題 |
|---|---|
| 第 1 週 | Introductory lecture and a survey on statistical knowledge |
| 第 2 週 | Probability theory: basic concepts (Pishro-Nik: Chapter 1, 2) |
| 第 3 週 | Random variables; probability distributions (Freund: Chapter 3, 4) In class exercise: estimate probability yourself |
| 第 4 週 | Discrete random variables: Probability mass functions ============== Quiz 1. ============== |
| 第 5 週 | Continuous random variables: Probability density functions (Pishro-Nik: Chapter 12, 13) Intro to MATLAB and R ============== Quiz 2. ==============Continuous random variables: Probability density functions; Intro to MATLAB and R ============== Quiz 2. ============== |
| 第 6 週 | Sampling distributions (Freund: Chapter 8) ==================== Lab 1 distributed ====================Sampling distributions (Freund: Chapter 9) ================== Lab 1 distributed |
| 第 7 週 | 校際活動週 No class ==================== Lab 1 due ====================校際活動週 No class ================== Lab 1 due |
| 第 8 週 | Hypothesis testing: theory (Freund: Chapter 12) ==================== Lab 2 distributed ====================Hypothesis testing: theory (Freund: Chapter 9) ================== Lab 2 distributed |
| 第 9 週 | Hypothesis testing: applications (Howell: Chapter 7; Freund: Chapter 13) ==================== Lab 2 due ====================Hypothesis testing: applications (Howell: Chapter 7; Freund: Chapter 13) ================== Lab 2 due |
| 第 10 週 | Estimation: theory and applications (Freund: Chapter 10, 11) ==================== Lab 3 distributed ==================== Midterm distributed ====================Estimation: theory and applications (Freund: Chapter 10, 11) ==================== Lab 3 distributed ==================== Midterm distributed |
| 第 11 週 | Linear regression and correlation (Howell: Chapter 9; Freund: Chapter 14) ==================== Lab 3 due ====================Regression 1 (Howell: Chapter 9; Freund: chapter 14) ==================== Lab 3 due |
| 第 12 週 | Multiple regression (Howell: Chapter 15)Regression 2 (Howell: Chapter 10) |
| 第 13 週 | Multilevel/hierarchical regression 1 (Gelman & Hill: Chapter 11, 12)Regression 3 (Howell: chapter 15) ==================== Midterm due |
| 第 14 週 | Multilevel/hierarchical regression 2 (Gelman & Hill: Chapter 13, 16)Generalized Linear Models ================== Lab 4 distributed |
| 第 15 週 | Non-parametric tests (Freund: Chapter 16; Howell: Chapter 18)Non-parametric tests ================== Lab 4 due |
| 第 16 週 | Review ==================== Final distributed ====================Review ================== Final distributed |
| 第 17 週 | 自主學習(optional lecture on ANOVA; Howell: Chapter 11) 自主學習 |
| 第 18 週 | 自主學習(optional lecture on Markov Chain Monte Carlo; Pishro-Nik: Chapter 11)自主學習 |
Howell, D.C. Statistical methods for psychology. Wadsworth Publishing. Freud, E. Mathematical statistics. Prentice-Hall. Pishro-Nik, H. Introduction to probability, statistics and random processes. Kappa Research, LLC. Gelman, A., Hill, J. Data analysis using regression and multilevel/hierarchical models. Cambridge University Press.