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

陳孜圩(Tzu-yu Chen)

指導教授 ： 張憶壽 ； 趙一峰

國立中央大學/理學院/數學系/碩士(2008年)

摘要

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。

關鍵字

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

並列摘要

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.

並列關鍵字

Markov chain Monte Carlo ； change point problem ； comparative genomic hybridization ； step function ； Bayesian regression model

參考文獻

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[4] Robert, Christian P.; Casella, George. (2004). Monte Carlo statistical methods. Springer Texts in Statistics. Springer-Verlag, New York.

[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.

[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.