課程資訊

Statistics

105-2

MATH3601

201 38100

3.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1052MATH3601_

Contents:
review of probability theory; distributions derived from the normal distribution; sample mean and sample variance; survey sampling; method of moments; method of maximum likelihood; bootstrap; efficiency; sufficiency; information bounds; hypothesis testing; likelihood ratio tests; goodness-of-fit tests; summarizing data; comparing two samples; analysis of variance; linear least squares; decision theory; Bayesian inference.

Teach the fundamentals of theoretical statistics.
Provide excellent preparation for advanced work in statistics and machine learning.

calculus, introduction to probability theorey.

Office Hours

Textbook: Rice, John A. (2007). Mathematical statistics and data analysis. Third edition. Brooks/Cole.

(僅供參考)

 No. 項目 百分比 說明 1. Homework and Quiz 30% 2. Midterm Exam 30% 3. Final Exam 40%

 課程進度
 週次 日期 單元主題 第1週 2/21,2/23 review of probability: random variables, joint distribution, expected values. approximate methods 第2週 2/28,3/02 limit theorem, distributions derived from the normal distribution (2/28 放假日) 第3週 3/07,3/09 survey sampling, simple random sampling (3/07 Quiz 1: Ch1-Ch4) 第4週 3/14,3/16 estimation of a ratio, stratified random sampling, fitting of probability distributions 第5週 3/21,3/23 自主學習週 第6週 3/28,3/30 parameter estimation, the method of moments, the method of maximum likelihood (3/28 Quiz 2: Ch5-Ch7) 第7週 4/04,4/06 MLE of multinomial cell probabilities, large sample theory for MLE (4/04 放假日) 第8週 4/11,4/13 confidence intervals from MLE, the Bayesian approach to parameter estimation 第9週 4/18,4/20 efficiency and the Cramer-Rao lower bound, sufficiency, uniformly minimum variance unbiased estimators 第10週 4/25,4/27 4/27 Midterm 第11週 5/02,5/04 hypothesis testing, likelihood ratio tests, Neyman-Pearson Lemma, p-value approach, uniformly most powerful tests 第12週 5/09,5/11 the duality of confidence intervals and hypothesis tests, generalized likelihood ratio tests, likelihood ratio tests for the multinomial distribution, the Poisson dispersion test 第13週 5/16,5/18 summarizing data, comparing two independent samples with normal assumptions (5/16 Quiz 3: Ch9) 第14週 5/23,5/25 Mann-Whitney test, comparing paired samples, signed rank test 第15週 5/30,6/01 analysis of variance: one-way layout (5/30 放假日) 第16週 6/06,6/08 analysis of variance: two-way layout 第17週 6/13,6/15 linear regression (6/15 Quiz 4) 第18週 6/22 6/22 Final