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

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Course Aims

This course introduces the mathematical foundations of statistics, including the design of statistical procedures and the analysis of real-world data. Topics include: elements of probability theory; statistical inference; unbiased estimator; Fisher information; Cramer-Rao inequality; confidence interval; statistical tests; Neyman-Pearson lemma; linear regression.

Key Features

Lecture notes and assignments are uploaded on the web-site. While the main focus of the course is to introduce the mathematical basis of statistics, some examples using real-world data will also be shown.

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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 (Cramer-Rao inequality)
7 Confidence interval I (estimation with confidence)
8 Confidence interval II (confidence interval and the t-distribution)
9 Hypothesis Testing I (null hypothesis and alternative hypothesis)
10 Hypothesis testing II (errors in statistical test)
11 Hypothesis testing III (optimality, Neyman-Pearson 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.

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