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系統識別號 U0026-0108201717361800
論文名稱(中文) 貝氏混合線性混合效應模型應用於美國職棒大聯盟球員薪資資料分析
論文名稱(英文) On Application of Bayesian Mixture of Linear Mixed-Effects Models to MLB Player Salaries
校院名稱 成功大學
系所名稱(中) 統計學系
系所名稱(英) Department of Statistics
學年度 105
學期 2
出版年 106
研究生(中文) 謝岱凌
研究生(英文) Tai-Ling Hsieh
學號 R26044051
學位類別 碩士
語文別 英文
論文頁數 28頁
口試委員 指導教授-李國榮
口試委員-陳瑞彬
口試委員-張升懋
中文關鍵字 貝氏變數選擇  馬可夫鏈  混合效應模型  混合模型 
英文關鍵字 Bayesian Variable selection  MCMC  Mixed-effects models  Mixture models 
學科別分類
中文摘要 我們的目的在於應用有限混合線性混合效應模型,並使用貝氏變數選擇方法來選出重要的固定效應和隨機效應。其中,引入潛在的變數來分類所觀測的對象,並便於在長期追蹤資料中辨別有影響力的固定和隨機效應。另外,使用尖峰和平面(spike-and-slab)的先驗分配所估計的迴歸係數來避免變數中潛在的高共線性,並在變數選擇問題中處理p>n。我們使用馬可夫鏈(MCMC)的抽樣技巧來做後驗分配的推論,並探討所提出模型在模擬數據上的準確性。兩個實際資料中,MLB球員薪資資料和精神病學資料用於解釋所提出的模型在實際應用中的困難和局限。
英文摘要 We consider Bayesian variable approaches to simultaneous selection of important fixed and random effects in the finite mixture of linear mixed-effects models. Latent variables are introduced to classify the membership of observations and to facilitate the identification of influential fixed and random components in the longitudinal data. A spike-and-slab prior for the regression coefficients is adopted to sidestep the potential complications of highly collinear covariates and to handle p>n in the variable selection problems. We employ Markov chain Monte Carlo (MCMC) sampling techniques for posterior inferences and explore the performance of the proposed model on simulated data. Two actual datasets, MLB salary data and psychiatric data, are used to explain the difficulties and limitations of the proposed model in real applications.
論文目次 Table of Contents
摘要.............................................i
Abstract........................................ii
誌謝............................................iii
Table of Contents...............................iv
List of Tables...................................v
Chapter 1. Introduction and Literature Review....1
Chapter 2. Methodology...........................4
2.1 Statistical Modelling........................4
2.2 Priors distribution..........................6
2.3 Posterior Computation and Inferences.........6
2.4 Full Conditionals...........................10
2.5 Label Switching.............................17
Chapter 3. Simulation Studies...................19
Chapter 4. Empirical Studies....................24
4.1 MLB Players’ Salaries.......................24
4.2 Drug Plasma Levels and Clinical Response....25
4.3 Results.....................................26
Chapter 5. Conclusion and Future Work...........27
References......................................28
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