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| 研究生： |
陳亭霓 Chen, Ting-Ni |
|---|---|
| 論文名稱： |
貝氏受限變數選擇於有序 probit 模型 Bayesian Constrained Variable Selection for Ordinal Probit Models |
| 指導教授： |
陳瑞彬
Chen, Ray-Bing 李國榮 Lee, Kuo-Jung |
| 學位類別： |
碩士 Master |
| 系所名稱： |
管理學院 - 數據科學研究所 Institute of Data Science |
| 論文出版年： | 2026 |
| 畢業學年度： | 114 |
| 語文別： | 中文 |
| 論文頁數： | 54 |
| 中文關鍵詞： | 有序Probit迴歸 、貝氏變數選擇 、約束型變數選擇 、Gibbs抽樣 |
| 外文關鍵詞： | Ordinal probit regression model, Bayesian variable selection, Constrained variable selection, Gibbs sampler |
| 相關次數： | 點閱：46 下載：0 |
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有序Probit 迴歸模型適用於反應變數為有序類別變數的情境。在此架構下，本研究以指標型貝氏變數選擇為基礎，引入約束型群組選擇方法，使模型得以同時處理變數間的群組關係、階層關係以及互斥關係，並透過馬可夫鏈蒙地卡羅(MCMC)方法抽樣後驗分配進行變數選擇與模型估計。模擬研究結果顯示，在涵蓋群組、階層、互斥約束及高維度等多種情境下，約束型群組選擇方法多數情況下能更準確地選出真正具有意義的變數。在帕金森氏症患者之影像資料的實際應用中，加入結構約束後不僅預測準確率提升，所選出的變數之間的關係亦更符合實務意義。
The ordinal probit regression model is suitable for situations where the response variable is ordinal categorical. In this study, we extend the indicator-based Bayesian variable selection approach by incorporating a constrained group selection method. This extension enables the model to simultaneously account for group relationships, hierarchical structures, and anti-hierarchical, with posterior inference conducted via an Markov Chain Monte Carlo (MCMC) method. Simulation results demonstrate that, under various scenarios involving group, hierarchical, and mutual exclusion constraints as well as high-dimensional settings, the proposed constrained group selection method more accurately identifies truly relevant variables in most cases. In the real data, the inclusion of structural constraints not only improves classification accuracy but also produces a set of selected variables whose relationships are more consistent with established domain knowledge.
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