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Pages
Posts
Progress on the ctGP Toolbox
Published:
The ctGP project began as an R implementation for category tree Gaussian process modeling. Over time, the computational core has been gradually redesigned and moved toward C++, with the goal of making the tool more efficient, extensible, and suitable for repeated use in practical modeling and optimization workflows.
biography
courses
Theory of Statistical Inference I
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Fall 2025 · Department of Mathematics, National Central University
Theory of Statistical Inference II
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Spring 2026 · Department of Mathematics, National Central University
Statistical Machine Learning
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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.
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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.
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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.
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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.
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talks
The 27th South Taiwan Statistics Conference
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2021 年統計學術研討會暨台、日、韓國際統計學術研討會
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The 31st South Taiwan Statistics Conference
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IASC-ARS Interim Conference 2023
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IASC-ARS Interim Conference 2024
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Multi-Fidelity Category-Tree Gaussian Process Modeling with Many Categorical Combinations
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Contributed talk at SRC 2026.
Multi-Objective Bayesian Optimization of CPU Cooling Design with Mixed Variables using Category Tree Gaussian Process
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Scheduled invited talk at the 35th South Taiwan Statistics Conference.
Objective-Wise Category Tree Gaussian Processes for Mean–Dispersion Bayesian Optimization
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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。