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課程名稱 |
統計學
Statistics |
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開課學期 |
105-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
鄭明燕 |
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課號 |
MATH3601 |
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課程識別碼 |
201 38100 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期二5(12:20~13:10)星期四8,9(15:30~17:20) |
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上課地點 |
天數102天數102 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1052MATH3601_ |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
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. |
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課程目標 |
Teach the fundamentals of theoretical statistics.
Provide excellent preparation for advanced work in statistics and machine learning. |
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課程要求 |
calculus, introduction to probability theorey. |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
Textbook: Rice, John A. (2007). Mathematical statistics and data analysis. Third edition. Brooks/Cole. |
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參考書目 |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Homework and Quiz |
30% |
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2. |
Midterm Exam |
30% |
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3. |
Final Exam |
40% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/21,2/23 |
review of probability: random variables, joint distribution, expected values. approximate methods |
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第2週 |
2/28,3/02 |
limit theorem, distributions derived from the normal distribution
(2/28 放假日) |
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第3週 |
3/07,3/09 |
survey sampling, simple random sampling
(3/07 Quiz 1: Ch1-Ch4) |
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第4週 |
3/14,3/16 |
estimation of a ratio, stratified random sampling, fitting of probability distributions |
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第5週 |
3/21,3/23 |
自主學習週 |
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第6週 |
3/28,3/30 |
parameter estimation, the method of moments, the method of maximum likelihood
(3/28 Quiz 2: Ch5-Ch7) |
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第7週 |
4/04,4/06 |
MLE of multinomial cell probabilities, large sample theory for MLE
(4/04 放假日) |
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第8週 |
4/11,4/13 |
confidence intervals from MLE, the Bayesian approach to parameter estimation |
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第9週 |
4/18,4/20 |
efficiency and the Cramer-Rao lower bound, sufficiency, uniformly minimum variance unbiased estimators |
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第10週 |
4/25,4/27 |
4/27 Midterm |
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第11週 |
5/02,5/04 |
hypothesis testing, likelihood ratio tests, Neyman-Pearson Lemma, p-value approach, uniformly most powerful tests |
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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 |
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第13週 |
5/16,5/18 |
summarizing data, comparing two independent samples with normal assumptions (5/16 Quiz 3: Ch9) |
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第14週 |
5/23,5/25 |
Mann-Whitney test, comparing paired samples, signed rank test |
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第15週 |
5/30,6/01 |
analysis of variance: one-way layout
(5/30 放假日) |
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第16週 |
6/06,6/08 |
analysis of variance: two-way layout |
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第17週 |
6/13,6/15 |
linear regression (6/15 Quiz 4) |
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第18週 |
6/22 |
6/22 Final |
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