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Graduate School
Mathematical Information Studies 9
Takafumi KANAMORI Associate Professor
Department: School of Informatics and Sciences
Class Time:  2011 Fall Thursday 
Recommended for:  School of Infomatics and Science 
Course Overview
Course Aims
This course introduces the mathematical foundations of statistics, including the design of statistical procedures and the analysis of realworld data. Topics include: elements of probability theory; statistical inference; unbiased estimator; Fisher information; CramerRao inequality; confidence interval; statistical tests; NeymanPearson lemma; linear regression.
Key Features
Lecture notes and assignments are uploaded on the website. While the main focus of the course is to introduce the mathematical basis of statistics, some examples using realworld data will also be shown.
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Syllabus
Course Objectives
To understand the mathematical foundations of statistics and various applications of data analysis.
Course Requirements and Recommended Courses
Prior basic knowledge of analytics, linear algebra and probability is recommended.
Textbook
No textbooks are assigned.
Course Schedule
Session  Contents 

1  Guidance 
2  Elements of probability I 
3  Elements of probability II 
4  Statistical inference I (unbiased estimator) 
5  Statistical inference II (Fisher information) 
6  Statistical inference III (CramerRao inequality) 
7  Confidence interval I (estimation with confidence) 
8  Confidence interval II (confidence interval and the tdistribution) 
9  Hypothesis Testing I (null hypothesis and alternative hypothesis) 
10  Hypothesis testing II (errors in statistical test) 
11  Hypothesis testing III (optimality, NeymanPearson lemma) 
12  Linear regression I (inference of regression function) 
13  Linear regression II (confidence interval and statistical test in linear regression) 
14  Maximum likelihood estimator I (maximum likelihood estimator) 
15  Maximum likelihood estimator II (exponential family) 
Grading
Grading will be based on homework assignments.
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Page last updated February 1, 2011
The class contents were most recently updated on the date indicated. Please be aware that there may be some changes between the most recent year and the current page.