SM512 ทฤษฎีสถิติ

(Statistical Theory)

ปีการศึกษา 2565

Instructor: รศ. ดร. วีระชาติ กิเลนทอง (tee@riped.utcc.ac.th) และ ดร.สัจจา ดวงชัยอยู่สุข (kei@riped.utcc.ac.th)

Course Schedule: Saturday 9.00 am – 12.00 pm Room 5401

TAs: คุณธนาธร มหาโยธา (ThanathonM.riped@gmail.com)


วิชานี้นำเสนอทฤษฎีและหลักการทางสถิติและความน่าจะเป็นที่จำเป็นสำหรับการวิเคราะห์ทางวิศวกรรมการเงิน โดยเริ่มจากหลักการพื้นฐานของทฤษฎีความน่าจะเป็น (probability theory) ความน่าจะเป็นแบบมีเงื่อนไข (conditional probability) ตัวแปรสุ่มและการแจกแจง (random variables and their distributions) ค่าคาดหมายและโมเมนต์ของตัวแปรสุ่ม (expectation and moments) คุณสมบัติและรูปแบบของการแจกแจงที่ได้รับความนิยมเป็นพิเศษ (special distributions) ทฤษฎีบทสำคัญในทางสถิติ 1) Law of Large Number 2) Central Limit Theorem ซึ่งจะบ่งบอกถึงคุณสมบัติของค่าเฉลี่ยเมื่อกลุ่มตัวอย่างมีขนาดใหญ่มาก การประมาณค่าพารามิเตอร์ด้วยวิธีแบบ maximum likelihood estimation และ Bayes estimation การแจกแจงของตัวประมาณค่า (sampling distributions of estimators) หลักการของการทดสอบสมมุติฐาน (hypothesis testing) และอาจรวมถึงแบบจำลองทางสถิติแบบเชิงเส้น (linear statistical models) วิธีการประมาณค่าแบบ nonparametric

1. Course Objective

The aim of this course is to give master-level students an introduction to principles, theories, and tools in advanced statistical theory. Students will also learn how to apply statistical models with real data using STATA software.

3. Required Textbooks:

1. DeGroot, Morris H. and Mark J. Schervish. 2012. Probability and Statistics. 4th edition: Preason. [DS]

2. Hogg, Robert V., Allen T. Craig and Joseph W. McKean. 2005. Introduction to Mathematical Statistics. 6th edition, Pearson. [HCM]

Optional Textbooks:

  1. Ross, S. M. (2014). Introduction to Probability Models. Academic press.

Data Sources

We will provide relevant data through the course website: https://sites.google.com/riped.org/tee/teaching/statistics

Program Sources

Program STATA version 14

4. Grades and Requirements

Grades will be based on the following weights:

30% Assignment(s)

30% Mid-Term Exam

40% Final Exam

Tentative Grading Range:

85 – 100 A

80 – 84 B+

70 – 79 B

65 – 69 C+

55 – 64 C

50 – 54 D+

40 – 49 D

39 or less F

4.1. Assignment

Students will be assigned to complete 12-15 individual assignments during the semester. An assignment with the lowest score will be dropped when calculating the total score for each student. Note: Late submission of the assignments is not accepted; a score of zero will be recorded for such assignment.

4.2. Examination

There will be two examinations: a mid-term exam counting for 30% of the total points, and a final exam counting for 40% of the total points. If a student misses a regular examination without acceptable excuse, a score of zero will be recorded for the examination.

Problem Assignments

1. Problem Assignment 1 (Due on August 27, 2022 at the beginning of the class).

2. Problem Assignment 2 (Due on September 3, 2022 at the beginning of the class).

3. Problem Assignment 3 (Due on September 10, 2022 at the beginning of the class).

4. Problem Assignment 4 and Dataset for Assignment (Due on September 17, 2022 at the beginning of the class).

5. Problem Assignment 5 (Due on September 24, 2022 at the beginning of the class).

6. Problem Assignment 6 and Dataset for Assignment (Due on October 1, 2022 at the beginning of the class).

7. Problem Assignment 7 and Dataset for Assignment (Due on October 8, 2022 at the beginning of the class).

8. Problem Assignment 8 and Dataset for Assignment (Due on October 15, 2022 at the beginning of the class).

9. Problem Assignment 9 (Due on October 29, 2022 at the beginning of the class).

10. Problem Assignment 10 (Due on November 5, 2022 at the beginning of the class).

11. Problem Assignment 11 (Due on November 12, 2022 at the beginning of the class).

12. Problem Assignment 12 (Due on November 19, 2022 at the beginning of the class).

13. Problem Assignment 13 and Dataset for Assignment (Due on November 26, 2022 at the beginning of the class).

14. Problem Assignment 14 and Dataset for Assignment (Due on December 10, 2022 at the beginning of the class).

15. Problem Assignment 15 and Dataset for Assignment (Due on December 10, 2022 at the beginning of the class).


Course Schedule

The course will be carried out in 15 sessions, totalling 45 lecture hours. The structure of the course is subject to revision if necessary (e.g., to conform to the background, knowledge, and interests of the students). The tentative structure of the whole course is as follows:

  1. Week 1 (August 20, 2022) : Basic Probability Theory. Reading Materials: Lecture Note.

  2. Week 2 (August 27, 2022) : Conditional Probability. Reading Materials: use the same Lecture Note as week 1.

  3. Week 3 (September 3, 2022) : Random Variables and Distributions. Reading Materials: Lecture Note.

  4. Week 4 (September 11, 2022) : Joint Distributions and Conditional Distributions. Reading Materials: use the same Lecture Note as week 3.

  5. Week 5 (September 17, 2022) : Statistical Independence and Distribution of Function of Random Variables. Reading Materials: use the same Lecture Note as week 3.

  6. Week 6 (September 24, 2022) : Expectation and Variance of Radom Variable. Reading Materials: Lecture Note.

  7. September 30, 2022 : MIDTERM EXAM (6.30 pm to 9.30 pm Room 5304)

  8. Week 7 (October 1, 2022) : Covariance, Correlation, and Moments. Reading Materials: use the same Lecture Note as week 6.

  9. Week 8 (October 8, 2022) : Normal Distributions and Popular Distributions. Reading Materials: Lecture Note.

  10. Week 9 (October 15, 2022) : Conditional Expectation. Reading Materials: use the same Lecture Note as week 6.

  11. Week 10 (October 29, 2022) : Large-Sample Theories. Reading Materials: Lecture Note.

  12. Week 11 (November 5, 2022) : Point Estimation: Bayes and MLE Estimations. Reading Materials: Lecture Note.

  13. Week 12 (November 12, 2021) : Hypothesis Testing. Reading Materials: Lecture Note.

  14. Week 13 (November 19, 2022) : Simple Regression Model.

  15. Week 14 (November 26, 2022) : Mutiple Regression Model: Estimation.

  16. Week 15 (December 10, 2022) : Mutiple Regression Model: Inference.


Computer Codes

The course will STATA program as the main statistical tool. Here are slides presentations for the STATA coding tutorials.

  1. STATA Code Lecture 1.

  2. STATA Code Lecture 2.

  3. STATA Code Lecture 3.

  4. STATA Code Lecture 4.

  5. STATA Code Lecture 5.

  6. STATA Code Lecture 6.