﻿ Mathematical Information Studies 9 | School of Informatics and Sciences | NU OCW
• Browse by Category
• Browse by 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 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.

Close Section

## 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 (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)