Posts by Collection
biography
courses
Theory of Statistical Inference I
Published:
Fall 2025 · Department of Mathematics, National Central University
Theory of Statistical Inference II
Published:
Spring 2026 · Department of Mathematics, National Central University
Statistical Machine Learning
Published:
Spring 2026 · Department of Mathematics, National Central University
portfolio
publications
Heterogeneous Treatment Effects on Cardiovascular Diseases With Dipeptidyl Peptidase-4 Inhibitors Versus Sulfonylureas in Type 2 Diabetes Patients
Published in Clinical Pharmacology & Therapeutics (CPT), 2020
Recommended citation: Yang, C.Y., Lin, W.A., Su, P.F., Li, L.J., Yang, C.T., Ou, H.T. and Kuo, S. (2021). "Heterogeneous Treatment Effects on Cardiovascular Diseases With Dipeptidyl Peptidase-4 Inhibitors Versus Sulfonylureas in Type 2 Diabetes Patients" Clinical Pharmacology & Therapeutics (CPT). 109(3):772-781.
Download Paper
Risk Assessment and Enhancement Suggestions for Automated Driving Systems through Examining Testing Collision and Disengagement Reports
Published in Journal of Advanced Transportation, 2023
Recommended citation: Wu, K.W., Wu, W.F., Liao, C.C., Lin, W.A. (2023). "Risk Assessment and Enhancement Suggestions for Automated Driving Systems through Examining Testing Collision and Disengagement Reports" Journal of Advanced Transportation. 3215817, 18 pages.
Download Paper
Category tree Gaussian process for computer experiments with many-category qualitative factors and application to cooling system design
Published in Journal of Quality Technology, 2024
Recommended citation: Lin, W.A., Sung, C.L., Chen, R.B. (2024). "Category tree Gaussian process for computer experiments with many-category qualitative factors and application to cooling system design." Journal of Quality Technology. 56(5):391-408.
Download Paper
On the Proper Orthogonal Decomposition-based emulation of spatio-temporal evolutions of turbulent wakes with fundamental frequencies
Published in American Institute of Aeronautics and Astronautics (AIAA) Journal, 2025
Recommended citation: Chang, C.M., Chiu, T.Y., Cheng, C.J., Tsai, H.Y., Lin, W.A., Chen, R.B. Chou, Y.J. (2025). "On the Proper Orthogonal Decomposition-based emulation of spatio-temporal evolutions of turbulent wakes with fundamental frequencies." American Institute of Aeronautics and Astronautics (AIAA) Journal. 63(9):3582-3594.
Download Paper
talks
The 27th South Taiwan Statistics Conference
Published:
2021 年統計學術研討會暨台、日、韓國際統計學術研討會
Published:
The 31st South Taiwan Statistics Conference
Published:
IASC-ARS Interim Conference 2023
Published:
IASC-ARS Interim Conference 2024
Published:
Multi-Fidelity Category-Tree Gaussian Process Modeling with Many Categorical Combinations
Published:
Contributed talk at SRC 2026.
Multi-Objective Bayesian Optimization of CPU Cooling Design with Mixed Variables using Category Tree Gaussian Process
Published:
Scheduled invited talk at the 35th South Taiwan Statistics Conference.
Objective-Wise Category Tree Gaussian Processes for Mean–Dispersion Bayesian Optimization
Published:
Scheduled invited talk at the 2026 Annual Meeting of the Chinese Statistical Association and NCCU Department of Statistics 60th Anniversary International Conference.
teaching_topics
條件機率，資訊進來以後，機率如何改變
Published:
條件機率描述在已知某個事件已經發生之後，我們如何重新評估另一個事件的機率。本篇從資訊的意義出發，介紹條件機率、乘法原理與廣義乘法原理。
哪些集合可以被賦予機率，事件集合族與 $\sigma$-域
Published:
樣本空間只說明隨機實驗的所有可能結果；事件集合族則說明哪些由結果構成的集合值得被賦予機率。本篇以 $\sigma$-域作為可測事件的清單，說明可測空間與機率空間的第一層結構。
機率如何被指定，古典機率、計數測度與幾何機率
Published:
公理化機率給出合法機率函數的條件，卻不直接說明機率應該怎麼算。本篇以古典機率、計數測度、幾何機率、客觀機率與主觀機率說明不同的指定方式。
由公理推出機率運算，餘事件、單調性與加法原理
Published:
Kolmogorov 公理本身很短，卻能推出一整套機率運算規則。本篇從虛無事件、有限可加性與餘事件公式開始，進一步整理單調性、加法原理、排容原理與常用機率不等式。
機率論的起點，隨機實驗、樣本空間與事件
Published:
機率論可從一個可重複、結果不確定、但所有可能結果可先描述的隨機實驗開始。樣本空間負責收納所有可能結果，事件則是我們真正關心的那些結果集合。
分割與全機率定理，從分類到加總
Published:
當樣本空間被一組互斥且周延的事件分割時，事件可以被拆成互斥片段；全機率定理將各來源的貢獻加總，並為辛普森悖論與貝氏定理提供共同骨架。
貝氏定理，資訊如何帶來更新
Published:
貝氏定理把全機率定理反過來讀。當某個結果已經被觀察到時，它說明我們如何重新分配對不同可能來源的相信程度。
分組、混合與辛普森悖論
Published:
同一個比較在每個分組內都成立，混合後卻可能反向。辛普森悖論說明，條件機率與全機率定理不只用來計算，也用來檢查比較是否公平。
獨立性，資訊不再改變機率
Published:
獨立性描述的是一種特別的資訊關係。若知道事件 B 發生後，事件 A 的機率完全不變，則 B 對 A 沒有提供新的機率資訊。
累積分配函數如何累積機率
Published:
CDF 描述隨機變數不超過門檻 x 的事件機率；離散型靠單點機率加總，連續型靠密度面積積分。
隨機變數，從樣本空間到數線
Published:
事件機率把事件送到機率數值；隨機變數則先把樣本點送到實數，使我們可以用數線、函數與微積分方法描述機率。
離散型隨機變數與機率質量函數
Published:
離散型隨機變數的機率集中在有限或可數個取值上。PMF 記錄各單點機率，事件機率則由對應單點機率加總取得。
連續型隨機變數與機率密度函數
Published:
連續型隨機變數的單點不具有正機率，事件機率改由密度函數在區間上的面積計算。PDF 可視為 CDF 的變化率，區間機率則由積分取得。
期望值，隨機變數的平均位置
Published:
分佈說明隨機變數的機率如何分佈在數線上。期望值則依照這些機率作加權平均，給出隨機變數的平均位置。離散型以 PMF 加總，連續型以 PDF 積分。
變異數與標準差
Published:
期望值給出隨機變數的平均位置。變異數則衡量隨機變數離開此平均位置的平均程度，標準差再把單位還原回原來的尺度。
混合型隨機變數
Published:
混合型隨機變數同時具有單點機率與連續密度。CDF 可同時呈現跳躍與連續累積，計算時則把離散部分加總、連續部分積分。