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課程名稱 |
高等統計推論一
Advanced Statistical Inference (Ⅰ) |
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開課學期 |
100-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
陳 宏 |
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課號 |
MATH7603 |
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課程識別碼 |
221 U1570 |
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班次 |
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學分 |
3 |
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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 |
星期一4(11:20~12:10)星期四7,8(14:20~16:20) |
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上課地點 |
天數304天數304 |
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備註 |
研究所統計科學組基礎課。
總人數上限：30人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1001ASI |
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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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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
Contents:
1.Probabilities, random variables, and distributions.
2.Transformations and expectations.
3.Common families of distributions.
4.Multivariate probability distributions and related properties.
5.Random samples, sampling distributions, and convergence concepts.
6.Sufficiency, likelihood, and equivalence principals. |
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課程目標 |
The objective of this course is to introduce to the students some basic theory of probability. It is fundamentally important for understanding the commonly used statistical concepts and methods. It also provides a necessary basis for students for a further study of other advanced statistical courses. |
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課程要求 |
Introduction to Probability and Statistics Theory or equivalent |
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預期每週課後學習時數 |
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Office Hours |
每週一 15:40~16:40
每週二 13:20~14:20
每週三 13:20~14:20
每週四 14:00~15:00 備註： 週一、週四 授課老師 (天文數學大樓465室) ; ??週二、週三 助教 (天文數學館???室) |
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指定閱讀 |
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參考書目 |
Textbook and References:
1. Casella, G. and Berger, R. L. (2002). Statistical Inference. 2nd ed. Duxbury Press.
2. Bickel, P. S. and Doksum, K. A. (2001). Mathematical Statistics: Basic Ideas and Selected Topics, Vol. I, 2nd ed. Prentice Hall.
3. Karr, A. F. (1993). Probability. Springer-Verlag.
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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. |
Homeworks |
20% |
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2. |
Midterm |
30% |
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3. |
Final |
30% |
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4. |
Quizzes |
20% |
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週次 |
日期 |
單元主題 |
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第1週 |
09/12 |
12日 中秋節(放假日)
Overview; Set Theory, Basics of Probability Theory |
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第2週 |
09/19 |
24日網路加選課程截止（中午12時截止）Conditional Probability and Independence, Random Variable, Density and Mass Functions |
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第3週 |
09/26 |
停修申請開始(至12月9日止);
Distributions of Functions of a Random Variable, Expected values |
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第4週 |
10/03 |
Moments and moment generating functions, Differentiating under an integral sign,
No class on Thursday. |
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第5週 |
10/10 |
雙十節; Discrete Distribution (Binomial, Poisson) Continuous Distribution (Uniform, exponential) |
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第6週 |
10/17 |
週一: Quiz 1,
週四: Exponential Families, Location and Scale Families, Inequalities and Identities 江老師授課 |
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第7週 |
10/24 |
Multiple random variables, Transformations, |
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第8週 |
10/31 |
Multiple Random Variables |
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第9週 |
11/07 |
Multiple Random Variables, Transformations, Hierarchical Models and Mixture Distributions, Covariance and Correlation |
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第10週 |
11/14 |
15日本校校慶(停課一天)。
17日期中考(Chapters 1 to 4.3及Theorem 4.4.3, 4.4.7, 4.5.3, 4.5.5, 4.5.6及 Definition 4.5.1, 4.5.2 )
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第11週 |
11/21 |
Convergence Concepts |
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第12週 |
11/28 |
Sums of Random Variables from a Random Sample,
Properties of the sample mean and variance |
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第13週 |
12/05 |
停修申請開始至12月9日止。Convergence Concepts |
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第14週 |
12/12 |
Order Statistics, Generating a random sample, Likelihood Principle,
Quiz 2 on December 12th (11:20-12:20; Chapter 4.4 to 4.6 and Chapter 5.1, 5.2, and 5.5) |
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第15週 |
12/19 |
Quiz 3 (Order Statistics, Generating random sample, Distributions related to normal and multivariate normal distribution, Convergence Concepts). |
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第16週 |
12/26 |
Methods of funding estimators, MLE, Method of Moments |
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第17週 |
2012/01/02 |
Sufficient Principle, Likelihood Principle, |
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第18週 |
01/09 |
週四: 期末考試。範圍為Chapters 4.4-6.1, 6.3.1, and 7.1-7.3.1(不含7.2.4), Metropolis Algorithm也不含. |
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