| Academic Year |
2024Year |
School/Graduate School |
School of Science |
| Lecture Code |
HB380000 |
Subject Classification |
Specialized Education |
| Subject Name |
確率統計特殊講義 |
Subject Name
（Katakana） |
カクリツトウケイトクシュコウギ |
Subject Name in
English |
Topics in Probability and Mathematical Statistics |
| Instructor |
IMORI SHINPEI |
Instructor
(Katakana) |
イモリ シンペイ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
4th-Year, First Semester, 1Term |
| Days, Periods, and Classrooms |
(1T) Mon5-6,Thur7-8：SCI E104 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
|
| Lecture |
| Credits |
2.0 |
Class Hours/Week |
|
Language of Instruction |
J
:
Japanese |
| Course Level |
5
:
Graduate Basic
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
|
| Keywords |
Hypothesis testing, Point estimation, Decision theory |
| Special Subject for Teacher Education |
|
Special Subject |
|
Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) | Mathematics
（Knowledge and Understanding）
・Acquiring knowledge and vision on advanced theories as an extension of core theory of modern mathematics. |
|---|
Class Objectives
/Class Outline |
Understand the formulation and optimization of statistical inference |
| Class Schedule |
Lecture 1
Least Squares (OLS) and Maximum Likelihood Estimation (MLE)
Lecture 2
Uniformly Minimum Variance Unbiased Estimator
Lecture 3
A Sufficient Statistics for a parameter
Properties of Sufficient Statistics
Lecture 4
Complete and Sufficient Statistics
The Exponential Family of Distributions
Lecture 5
Asymptotic Properties of MLEs
Lecture 6
Asymptotic Properties of MLEs: Consistency
Lecture 7
Asymptotic Properties of MLEs: Asymptotic Normality
Lecture 8
Interval estimation
Lecture 9
Hypothesis Testing
Lecture 10
Neyman-Pearson Theorem
Lecture 11
Most Powerful Tests
Uniformly Most Powerful Test
Lecture 12
Randomization Tests
Lecture 13
Unbiased Tests
Lecture 14
Likelihood Ratio Tests
Lecture 15
Two other tests related to likelihood
Report
The class schedule may be changed due to the progress. |
Text/Reference
Books,etc. |
確率・統計の数学的基礎（藤越，若木，柳原著：広島大学出版会）
If English textbooks are required, please let me know. |
PC or AV used in
Class,etc. |
|
| (More Details) |
Blackboard and PowerPoint slides will be used. |
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
Please do not hesitate to ask me if you have any (minor) questions. |
| Requirements |
|
| Grading Method |
Report (100%) |
| Practical Experience |
|
| Summary of Practical Experience and Class Contents based on it |
|
| Message |
|
| Other |
|
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. |