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研究生： 王志偉
Chih-Wei Wang
論文名稱：
Bayesian Prediction on Longitudinal Data with Random Effects Covariance Matrix
指導教授： 樊采虹
Tsai-Hung Fan
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 統計研究所
Graduate Institute of Statistics
畢業學年度： 95
語文別： 英文
論文頁數： 65
外文關鍵詞： Bayesian inference, Cholesky decomposition, Random effects, Mixed model, Markov chain Monte Carlo, Prediction
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    • 隨機效應混合模型是時常被用來建構長時期追蹤資料的一類普遍模型。在實驗對象之中，這些模型的隨機效應共變異矩陣典型地被假設為常數。這篇論文中，我們採用一種特殊的Cholesky矩陣分解法去建構隨機效應共變異矩陣而且允許這種分解中所引進的參數是依賴實驗對象特性共變數。一種跟隨著Metropolis-Hastings步驟的Gibbs抽樣方法在這裡被實行用來幫助我們作出貝氏推論。此外，對於每個實驗對象，根據先前已觀測到的資料去預測未來的觀測資料是我們的另一個主題。一些模擬上的研究將被實行用來驗證我們的方法論以及常態分配測量誤差模型與學生t分配測量誤差模型在這裡將被比較。

    Random effects (mixed) models are a common class of models used frequently to model longitudinal data. The random effects covariance matrix of these models is typically assumed constant across subject. In this thesis, we use a special Cholesky decomposition of the matrix to model the random effects covariance matrix and allow the parameters that result from this decomposition to depend on subject-specific covariates. A simple Gibbs sampler together with Metropolis-Hastings (M-H) steps can be implemented here to draw the Bayesian inference. Furthermore, predicting the future observations given the previous observed data for each subject is our another topic. Several simulation studies are carried out to demonstrate our methodologies and comparisons are make from both normal and t measurement error models.

    Introduction 1 1.1 Motivation and background ................................. 1 1.2 The random effects covariance matrix model ................ 3 1.3 Overview .................................................. 6 2 Bayesian Inference 8 2.1 Random effects model with normal measurement errors ....... 8 2.2 Random effects model with t measurement errors ............ 15 3 Prediction of Individual Trajectories 18 3.1 Prediction with normal measurement errors ................. 19 3.2 Prediction with t measurement errors ...................... 22 4 Simulation Study and Models Comparison 25 4.1 Simulation study I: normal measurement error model ........ 26 4.2 Simulation study II: t measurement error model ............ 28 4.3 Simulation study III: comparisons ........................ 29 5 Concluding Remarks 33 Appendix 35 References 36

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