Mathematics and Statistics for International Development Engineering Mathematics and Statistics for International Development Engineering

文字サイズ小中大

担当教員: 山下幸彦

使用教室: 木7-8(S611)

単位数: 講義：2 演習：0 実験：0

講義コード: 70042

シラバス更新日: 2011年9月30日

講義資料更新日: 2011年9月20日

学期: 後期

概要

講義概要

Linear algebra (eigenvalue problem, singular value decomposition,
and generalized inverse matrix), optimization technique (gradient method, conjugate gradient method, and quasi-Newton method), and statistics (estimation and test) are lectured.

講義の目的

The objective of this course is to provide fundamental optimization technique
and statistics to handle various quantities with respect to international development.
In order to understand those knowledges, basic mathematics for them is also provided.

講義計画

1. Introduction
2. Eigenvalue decomposition and singular value decomposition
3. Generalized inverses of matrix
4. Maximum gradient method and Conjugate gradient method
5. Newton method and Quasi-Newton method
6. Lagrange’s method and Karush–Kuhn–Tucker condition
7. Dual problem
8. Penalty method
9. Probability (Definition of Random variable)
10. Estimator (Maximum likelihood estimator and Bayesian estimator)
11. Cramer-Rao lower bound
12 Principle component analysis
13. Regression
14. Testing
15. Statistical learning theory

教科書・参考書等

Copy of slide is prepared

成績評価

Attendance
Homework
Report