本篇學位論文主要在探討有圖論結構的實驗設計與分析，其中包含了實驗單位元以及實驗因子的圖論結構造成的新型態實驗，分別稱作網絡實驗以及排序實驗。網絡實驗常見於現實生活中以人或人群為實驗單位元的實驗設計，並且在網路廣告的A/B測試當中尤為常見。而排序實驗則是常見於不同順序會產生出很不同的結果的實驗當中，例如藥物實驗和工作排程優化。

在新型態的實驗情境下，傳統的實驗設計已經不夠，因此我們討論了適合的新模型以及對其產生好處的新實驗設計。此外，我們的研究也包含了分析方法的優化，使得在廣義線性模型底下的變數選擇更有效果。在研究的過程中，我掌握了如何探討一個模型和一個設計為何存在的統計意義，也掌握了線性代數、圖論以及微積分的更多進階知識。

This dissertation primarily investigates experimental design and analysis with graph structures. It introduces novel types of experiments induced by the graph structure of experimental units and factors, referred to as network experiments and order-of-addition experiments, respectively. Network experiments are commonly seen in real-life experimental designs where individuals or groups serve as experimental units, particularly in A/B testing of online advertisements. Order-of-Addition experiments are typical in scenarios where different sequences can yield significantly different results, such as drug trials and job scheduling.

Given these novel experimental contexts, traditional experimental designs are no longer efficient. We discuss suitable new models and the corresponding good experimental designs based on these model. Additionally, our research includes the optimization of analysis methods, enhancing variable selection under generalized linear models. Throughout the research process, I have gained insights into defining models and designs, and have deepened my understanding of linear algebra, graph theory, and calculus.

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