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研究生： 陳孜圩
Tzu-yu Chen
論文名稱： 數據依賴誤差之階梯函數迴歸的貝氏方法
A Bayesian Approach to Step Function Regression with Data Dependent Error
指導教授： 張憶壽
I-Shou Chang
趙一峰
I-Feng Chao
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
畢業學年度： 96
語文別： 英文
論文頁數： 18
中文關鍵詞： 變點問題 、馬可夫鏈蒙地卡羅法 、階梯函數 、比較型基因體雜交分析技術 、貝氏迴歸模型
外文關鍵詞： Markov chain Monte Carlo, change point problem, comparative genomic hybridization, step function, Bayesian regression model
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    • 在這篇論文中，我們將 Wen et al. 在2006年提出的貝氏迴歸模型做推廣，考慮其誤差項會受到迴歸函數的函數值所影響。除此之外，我們也更近一步地探討，在每一個位置附近發生跳點的機率以及其所跳的高度之間的關係。

    One of the purposes of this thesis is to extend the Bayesian step-function regression model of Wen et al. (2006) to allow for more general noise term so that the error term may vary with the ratio itself, which is also a familiar phenomenon in regression analysis. The other purpose of this thesis is to explore in more detail the relation between the size of the jump at a point of the posterior mode and posterior probability that it is a jump point.

    中文摘要 ............................................................ i 英文摘要 ........................................................... ii 目錄 .................................................................. iii 1 Introduction ...................................................... 1 2 A Bayesian Regression Model Choice ............. 2 2.1 The model ...................................................... 2 2.2 Bayesian inference ......................................... 3 3 Simulation Studies ............................................ 9 3.1 Simulation 1 ................................................... 9 3.1.1 Parameters setting ....................................... 9 3.1.2 Monitoring convergence .............................10 3.1.3 Results ........................................................ 11 3.2 Simulation 2 .................................................. 13 3.2.1 Parameters setting .......................................13 3.2.2 Results ........................................................ 13 4 Discussion ........................................................ 17 References ........................................................... 18

    [1] Gelman, Andrew; Carlin, John B.; Stern, Hal S.; Rubin, Donald B. (2004). Bayesian data analysis. Second edition. Texts in Statistical Science Series. Chapman and Hall/CRC, Boca Raton, FL.
    [2] Green, Peter J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 , no. 4, 711{732.
    [3] Lai, Tze-Leung; Xing, Haipeng; Zhang, Nancy. (2007). Stochastic segmentation models for array-based comparative genomic hybridization data analysis. Biostatistics. Sep 12; : 17855472 (P,S,E,B,D)
    [4] Robert, Christian P.; Casella, George. (2004). Monte Carlo statistical methods. Springer Texts in Statistics. Springer-Verlag, New York.
    [5] Wen, Chi-Chung; Wu, Yuh-Jenn; Huang, Yung-Hsiang; Chen, Wei-Chen; Liu, Shu-Chen; Jiang, Shih Sheng; Juang, Jyh-Lyh; Lin, Chung-Yen; Fang,Wen-Tsen; Hsiung, Chao Agnes; and Chang, I-Shou. (2006). A Bayes regression approach to array-CGH data. Stat. Appl. Genet. Mol. Biol. 5 , Art. 3.

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