混合先驗分佈下誤差項為自我迴歸之線性混合效應模型的貝氏分析

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張逸塵(Yi-chen Zhang) 查詢紙本館藏

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統計研究所

論文名稱

混合先驗分佈下誤差項為自我迴歸之線性混合效應模型的貝氏分析
(Bayesian Inference on the Linear Mixed-Effect Models with Autoregressive Errors Using Mixture Priors)

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摘要(中)

本文主要目的在於探討誤差項具自我迴歸之貝氏線性混合效應模型。經由混合先驗分佈，找出顯著的固定效應與隨機效應變數，進而得到中位機率模型，並由該模型進行貝氏之推論與預測。最後將此模型應用在一組高血糖和相對高胰島素血症，對於葡萄糖的容忍度實驗之資料中，結果顯示，本文提出的方法可以提供準確的預測。

摘要(英)

In this thesis, we address the problem of Bayesian linear mixed effects model with auto-regressive errors. We consider a mixture prior to identify subsets of covariates having nonzero fixed effect coefficients or nonzero random effects variance, and eventually obtain a median probability model, which is utilized for Bayesian inference and prediction. Finally, the proposed method is applied to a study of the association of hyperglycemia and relative hyperinsulinemia, and it yields very accurate prediction results.

關鍵字(中)

★ 自我迴歸模型
★ 吉比氏抽樣法
★ 混合先驗分佈
★ 隨機效應
★ 固定效應
★ 貝氏預測
★ 中位機率模型

關鍵字(英)

★ Fixed effect
★ Random effect
★ Mixture prior
★ Gibbs sampling
★ AR(1) model
★ Median probability model
★ Bayesian prediction

論文目次

中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
誌謝辭. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
第一章緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 研究動機與背景. . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 文獻探討與方法回顧. . . . . . . . . . . . . . . . . . . . . . 4
1.3 研究方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
第二章混合先驗分佈下之貝氏線性混合效應模型. . . . . 7
2.1 貝氏線性迴歸模型. . . . . . . . . . . . . . . . . . . . . . . 8
2.2 貝氏線性混合效應模型. . . . . . . . . . . . . . . . . . . . . 12
2.3 中位機率模型. . . . . . . . . . . . . . . . . . . . . . . . . . 16
第三章誤差具自我迴歸的貝氏線性混合效應模型. . . . . 19
3.1 貝氏推論. . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.1 相關係數相同之模型. . . . . . . . . . . . . . . . . . 19
3.1.2 相關係數不同之模型. . . . . . . . . . . . . . . . . . 23
3.2 線性混合效應之中位機率模型. . . . . . . . . . . . . . . . . 25
3.3 貝氏預測. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
第四章模擬分析與實例應用. . . . . . . . . . . . . . . . . . 29
4.1 線性混合效應模型之模擬分析. . . . . . . . . . . . . . . . . 29
4.2 誤差具自我迴歸的線性混合效應模型之模擬分析. . . . . . . . 32
4.3 實例分析與預測. . . . . . . . . . . . . . . . . . . . . . . . 36
第五章結論. . . . . . . . . . . . . . . . . . . . . . . . . . . 42
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

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立中央大學統計研究所碩士論文。

指導教授

樊采虹、于振華
(Tasi-hung Fan、Jenn-hwa Yu)

審核日期

2009-6-22

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