Mathematical Statistics-E2

科目ナンバリング U-LAS11 10010 LE55 開講年度・開講期 2021 ・ 前期
単位数 2 単位 授業形態 講義
配当学年 主として2回生 対象学生 理系向
使用言語 英語 曜時限 木3
教員 Croydon, David Alexander (数理解析研究所 准教授)
授業の概要・目的 This course will develop the theory of statistical inference, which has applications across the natural and social sciences, and beyond. It will focus on the key topics of parameter estimation and hypothesis testing. As well as presenting the theoretical justification for various techniques covered, it will also be a goal to show how these can be applied in examples.
到達目標 - To understand the basic concepts of, and mathematical justification for, point estimation and hypothesis testing
- To be able to apply key techniques of statistical inference in applications
授業計画と内容 The following indicates possible topics that will be covered and approximate schedule, though the precise details may vary depending on the student's proficiency level and background.

(1) Review of probability theory [2 weeks]
Distribution and expectation, multivariate distributions, conditional distributions, notions of convergence, common families of distributions, random samples

(2) Point estimates [5 weeks]
Estimators, sampling distribution, parameterized statistical models, maximum likelihood estimates, sampling distributions, confidence intervals, point estimation for linear models

(3) Hypothesis testing [5 weeks]
Likelihood ratio tests, methods of evaluating tests, goodness of fit tests, tests for comparing mean and variance of two samples, tests for independence

(4) Applications [2 weeks]
Extended example applications of the main techniques covered earlier in the course

Total: 14 classes and 1 week for feedback
成績評価の方法・観点 There will be regular exercise sheets throughout the course, for which students will be expected to return work and present some of their answers in class. This will account for 70% of the final mark. The remaining 30% will be based on a final exam.

NB. In case a final exam is not possible, the written assignments will account for 100% of the final mark.
履修要件 No statistical knowledge will be assumed. However, some basic calculus (e.g. finding the maximum of a function using differentiation) will be helpful.
授業外学習(予習・復習)等 The lecturer will present the basic concepts in class, upon which assignments will be set. The time for these might vary from week to week, and student to student, but the lecturer estimates these to take 1-2 hours
教科書 There will be no set textbook for the course, as the lectures will contain all the material needed for the homework and exam. However, students might find the following useful as additional reading:

Statistical Inference, Casella and Berger, Duxbury, 2002