課程大綱

課程資訊

課程名稱

統計學二
Statistics (Ⅱ)

開課學期

114-2

授課對象

學程生物統計學程

授課教師

王仁

課號

Forest2032

課程識別碼

605 26220

班次

學分

3.0

全/半年

半年

必/選修

選修

上課時間

星期二8,9,10(15:30~18:20)

上課地點

新401

備註

森林生物學群、森林環境學群、資源保育及管理學群選擇必修。
總人數上限：30人

課程簡介影片

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課程大綱

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課程概述

This course focuses on the application of advanced statistical methods in forest science and ecological research. It introduces widely used tools such as Linear Mixed Models (LMMs), Generalised Linear Models (GLMs) and Random Forests, and also covers Principal Component Analysis (PCA) and non-parametric statistical techniques. Through hands-on work with real forest survey datasets and practical programming exercises, the course aims to equip students with the skills to apply statistical models flexibly in forestry and natural-resource management research.
本課程著重於進階統計方法在森林科學與生態研究中的應用。課程將介紹線性混合模型 (LMM)、廣義線性模型 (GLM)、隨機森林 (Random Forest) 等常用工具，並涵蓋主成分分析 (PCA) 與非參數統計方法。透過實際的森林調查數據操作與程式實作，本課程旨在培養學生能夠將統計模型靈活應用於林業與自然資源管理相關研究中。

課程目標

Students with prior background will, upon completing this course, are able to accurately interpret academic texts with statistical analyses and perform advanced statistical methods.
希望有基礎統計學背景的學生在完成本課程後，能夠準確地解釋學術文本的統計分析並執行進階的統計方法

課程要求

(1) Students must have access to a laptop or mobile device with R and R Studio installed.
學生需有筆記型電腦或其他行動裝置並安裝R 和Rstudio。
(2) A sustained enthusiasm for learning is expected throughout the course.
保持學習的熱誠。
(3) In cases of unavoidable absence, autonomy in practice must be undertaken to ensure examination performance meets the pass threshold.
如果翹課的話，至少要自主練習讓考試分數及格。

預期每週課前或/與課後學習時數

0.1 hr -14 hr

Office Hours

另約時間備註： Please make an appointment for a meeting if you like

指定閱讀

Textbook:
Everitt, B.S. & Hothorn, T. (2011). An Introduction to Applied Multivariate Analysis with R. Springer.

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2021). An Introduction to Statistical Learning with Applications in R (ISLR, 2nd ed.). Springer.

Zuur, A.F., Ieno, E.N., Walker, N., Saveliev, A.A., & Smith, G.M. (2009). Mixed Effects Models and Extensions in Ecology with R. Springer.

Classic papers and books:
Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5–32. https://doi.org/10.1023/A:1010933404324 (Random forests)

參考書目

Textbooks:
Glover, T., & Mitchell, K. (2015). An introduction to biostatistics (3rd ed.). Waveland Press.

Heumann, C., Schomaker, M., & Shalabh. (2017). Introduction to statistics and data analysis. Springer Nature. https://doi.org/10.1007/978-3-319-46162-5
Lepš, J., & Šmilauer, P. (2020). Biostatistics with R: An introductory guide for field biologists. Cambridge University Press. https://doi.org/10.1017/97811086160412

Ott, R. L., & Longnecker, M. (2016). An introduction to statistical methods & data analysis (7th ed.). Cengage Learning.

Ramsey, F., & Schafer, D. (2012). The statistical sleuth: A course in methods of data analysis (3rd ed.). Brooks Cole.

阿部真人 (2021). データ分析に必須の知識・考え方統計学入門仮説検定から統計モデリングまで重要トピックを完全網羅 [Essential Knowledge and Concepts for Data Analysis: Introductory Statistics—Comprehensive Coverage from Hypothesis Testing to Statistical Modeling]. ソシム.

久保拓彌 (2012). データ解析のための統計モデリング入門: 一般化線形モデル・階層ベイズモデル・MCMC [Introduction to statistical modeling for data analysis: Generalized linear models, hierarchical Bayesian models, and MCMC]. 岩波書店.

Classic papers and books:
Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5–32. https://doi.org/10.1023/A:1010933404324 (Random forests)

Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B (Methodological), 39(1), 1–22. https://doi.org/10.1111/j.2517-6161.1977.tb01600.x (EM algorithm for maximum likelihood)

Fisher, R. (1925). Theory of Statistical Estimation. Mathematical Proceedings of the Cambridge Philosophical Society, 22(5), 700–725. https://doi.org/10.1017/S0305004100009580

Gosset, W. S. (1908). The probable error of a mean. Biometrika, 6(1), 1–25. https://doi.org/10.2307/2331554 (Student’s t-test)

Hume, D. (1896). A treatise of human nature (L. A. Selby-Bigge, Ed.). Clarendon Press. (Original work published 1739-1740) (Constant conjunction)

Pearson, K. (1896). Mathematical contributions to the theory of evolution. III. Regression, heredity, and panmixia. Philosophical Transactions of the Royal Society of London, Series A, 187, 253–318. https://doi.org/10.1098/rsta.1896.0007 (Pearson correlation coefficient)

Popper, K. R. (1959). The logic of scientific discovery. Routledge. (Original work published 1934) ISBN: 978-0-415-27844-7 (The concept of falsifiability)

Royston, P. (1982). Algorithm AS 181: The W test for normality. Applied Statistics, 31, 176–180. https://doi.org/10.2307/2347986 (Shapiro-Wilk normality test)

Tukey, J. W. (1949). Comparing individual means in the analysis of variance. Biometrics, 5(2), 99–114. https://doi.org/10.2307/3001913 (Tukey’s honest significant difference, HSD)

Welch, B. L. (1951). On the comparison of several mean values: An alternative approach. Biometrika, 38, 330–336. https://doi.org/10.2307/2332579 (Welch's heteroscedastic F test)

Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80–83. https://doi.org/10.2307/3001968 (Wilcoxon signed rank test)

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	期中考	40%
2.	期末考	40%
3.	平時作業	20%

本校建議 A+ 比例上限為 20% ，非強制規定，授課教師可依課程要求調整，建議必修課程參考。
本校採用等第制評定成績，學生成績評量辦法中的百分制分數區間與單科成績對照表僅供參考，授課教師可依等第定義調整分數區間。詳見學習評量專區 (連結)。

針對學生困難提供學生調整方式

上課形式	提供學生彈性出席課程方式
作業繳交方式	學生與授課老師協議改以其他形式呈現
考試形式	延後期末考試日期(時間)
其他	由師生雙方議定

課程進度

週次	日期	單元主題
第1週	2/24	Course introduction and how to stand on the shoulders of giants (using LLM) to help with homework and learn R and python (good news for free people)
第2週	3/3	Do you believe in statistics? Begin your adventure with the most recent record. Task 1: Environment Setup & Packages Task 2: Review of statistical inference — prove the unbiasedness of X ˉand S^2.
第3週	3/10	Constructing sampling distributions — definitions and derivations of χ^2, t, and F distributions. Task 3: Derive the sampling distribution of the t-statistic.
第4週	3/17	The Japanese Forest Society Congress — no class this week.
第5週	3/24	Foundations of regression — OLS derivation; the Gauss–Markov theorem (BLUE); properties of residuals. Task 5: LR model
第6週	3/31	Multiple regression and model diagnostics — multicollinearity; residual checks; influence diagnostics. Task 6: allometric model for forest biomass.
第7週	4/7	Generalised Linear Models (GLMs) — exponential-family distributions; link functions; maximum-likelihood estimation. Task 7: GLM - Count data — Poisson regression.
第8週	4/14	GLMs (continued) — logistic regression; model diagnostics; overdispersion. Task 8: GLM - Probability of management treatment. Course review for the midterm exam.
第9週	4/21	Midterm exam. Task 9: take a rest
第10週	4/28	Linear Mixed Models (LMMs) — fixed vs random effects; nested structures; intraclass correlation (ICC). Task 10: LMMs.
第11週	5/5	Generalised Linear Mixed Models (GLMMs) — GLM extension with random effects; REML versus ML. Task 11: GLMMs.
第12週	5/12	Generalised Additive Models (GAMs) — spline bases; smooth terms; effective degrees of freedom. Task 12: GAMs.
第13週	5/19	GAMs with random effects (GAMMs) — combining smoothers and random effects; handling spatio-temporal correlation. Task 13: GAMMs.
第14週	5/26	Time-Series Analysis: A Case Study of Electricity Supply and Demand in Taiwan. (Real cases shared by Dr. Hsu at Chung-Hua Institution for Economic Research)
第15週	6/2	PCA & dimensionality reduction, Random forests, model validation, hybrid approaches — factor analysis and modelling. Course review and consolidation for the final exam.
第16週	6/9	Final exam.