數理統計
Mathematical statistics
| 節 | 週二 |
|---|---|
3 10:10–11:00 | 數理統計 YL839（陽明） 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. Students will learn theory, how to perform statistical analysis, and how to write computer code to perform statistical analysis. The course consists of lectures and in-class demonstrations. In-class demonstrations include coding demonstrations in MATLAB and R. The students will be given weekly lecture slides and codes (MATLAB and R). Throughout the semester, the students will be given 4 to 6 take-home lab exercises (depending on how the course progresses), a take-home midterm exam, and a take-home final exam. 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.
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In class quiz (10%); Lab exercises (30%, take-home); Midterm exam (30%, take-home); Final exam (30%, take-home).
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| 週次 | 主題 |
|---|---|
| 第 1 週 | Introductory lecture and a survey on statistical knowledge 2023-02-14(二) 時數：[2023-02-14]吳仕煒(2.00) |
| 第 2 週 | Probability theory: basic concepts (Pishro-Nik: Chapter 1, 2) 2023-02-21(二) 時數：[2023-02-21]吳仕煒(2.00) |
| 第 3 週 | • Random variables; probability distributions (Freund: Chapter 3, 4) • In class exercise: estimate probability yourself 2023-02-28(二) 時數：[2023-02-28]吳仕煒(2.00) |
| 第 4 週 | • Discrete random variables: Probability mass functions • Quiz 1 2023-03-07(二) 時數：[2023-03-07]吳仕煒(2.00) |
| 第 5 週 | • Continuous random variables: Probability density functions • Intro to MATLAB and R (Pishro-Nik: Chapter 12, 13) • Quiz 2 • Lab 1 distributed 2023-03-14(二) 時數：[2023-03-14]吳仕煒(2.00) |
| 第 6 週 | • Sampling distributions (Freund: Chapter 8) • Lab 1 due • Lab 2 distributed 2023-03-21(二) 時數：[2023-03-21]吳仕煒(2.00) |
| 第 7 週 | • Hypothesis testing: theory (Freund: Chapter 12) • Lab 2 due 2023-03-28(二) 時數：[2023-03-28]吳仕煒(2.00) |
| 第 8 週 | Holiday. No class. 2023-04-04(二) 時數：[2023-04-04]吳仕煒(0.00) |
| 第 9 週 | • Hypothesis testing: applications (Howell: Chapter 7; Freund: Chapter 13) 2023-04-11(二) 時數：[2023-04-11]吳仕煒(2.00) |
| 第 10 週 | • Estimation: theory and applications (Freund: Chapter 10, 11) • Lab 3 distributed • Midterm distributed 2023-04-18(二) 時數：[2023-04-18]吳仕煒(2.00) |
| 第 11 週 | • Linear regression and correlation (Howell: Chapter 9; Freund: Chapter 14) • Lab 3 due 2023-04-25(二) 時數：[2023-04-25]吳仕煒(2.00) |
| 第 12 週 | • Multiple regression (Howell: Chapter 15) 2023-05-02(二) 時數：[2023-05-02]吳仕煒(2.00) |
| 第 13 週 | • Multilevel/hierarchical regression 1 (Gelman & Hill: Chapter 11, 12) • Midterm due 2023-05-09(二) 時數：[2023-05-09]吳仕煒(2.00) |
| 第 14 週 | • Multilevel/hierarchical regression 2 (Gelman & Hill: Chapter 13, 16) • Lab 4 distributed 2023-05-16(二) 時數：[2023-05-16]吳仕煒(2.00) |
| 第 15 週 | • Non-parametric tests (Freund: Chapter 16; Howell: Chapter 18) • Lab 4 due • Lab 5 distributed 2023-05-23(二) 時數：[2023-05-23]吳仕煒(2.00) |
| 第 16 週 | • Review • Lab 5 due • Final exam distributed 2023-05-30(二) 時數：[2023-05-30]吳仕煒(2.00) |
| 第 17 週 | 2023-06-06(二) |
| 第 18 週 | 2023-06-13(二) |
1. Freund, E. Mathematical statistics. Prentice-Hall. 2. Gelman, A., Hill, J. Data analysis using regression and multilevel/hierarchical models. Cambridge University Press. 3. Howell, D.C. Statistical methods for psychology. Wadsworth Publishing. 4. Pishro-Nik, H. Introduction to probability, statistics ad random processes. Kappa Research, LLC.
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