臺灣博碩士論文加值系統

本文架構在聯合的平均向量與尺度共變異矩陣的多變量ｔ迴歸模
型下, 提出一個完全的貝氏方法來分析不完整的長期資料。為了計算上的便利和簡化理論推導，我們介紹兩個二元的輔助矩陣來指示應變數中觀察到與遺失的成分。為了計算參數的驗後分配, 我們使用馬可夫鏈蒙地卡羅方法發展一個有效率的資料擴增演算法。此外, 我們也考慮遺失反應變數的貝氏預測推論。最後, 這些透過一個長期睡眠剝奪的研究的真實例子來闡述所提出的方法。

In this thesis, we provide a fully Bayesian approach to multivariate t regression models with its mean vector and scale covariance matrix modeled jointly for analyzing incomplete longitudinal data. To facilitate the computation and simplify theoretic derivations, we introduce two binary auxiliary matrices for indexing the observed and missing components of the dependent variables. A computationally
flexible Markov chain Monte Carlo (MCMC) algorithm utilizing the data augmentation (DA) technique is implemented for computing the entire posterior distributions
of parameters. Bayesian predictive inferences for the unobserved responses are also investigated. The proposed methodologies are illustrated through a real example from a sleep dose-response study.

Contents
1. Introduction 1
2. Model with missing information 5
3. An efficient ECME procedure for ML estimation 7
4. Bayesian methodology 11
4.1. Prior settings, full conditionals and the DA algorithm . . . . . . . . . 11
4.2. Convergence assessment using multiple chains . . . . . . . . . . . . . 15
4.3. Bayesian model comparison: Deviance Information Criterion . . . . . 15
5. A numerical illustration 17
6. Concluding remarks 27
Appendix 28
Appendix A: Proof of Proposition 1. . . . . . . . . . . . . . . . . . . . . . 28
Appendix B: Proof of the Eq. (3.4) . . . . . . . . . . . . . . . . . . . . . . 30
Appendix C: Proof of Proposition 2. . . . . . . . . . . . . . . . . . . . . . 31
References 32

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