博碩士論文 93225024 詳細資訊




以作者查詢圖書館館藏 以作者查詢臺灣博碩士 以作者查詢全國書目 勘誤回報 、線上人數:9 、訪客IP:3.238.107.166
姓名 王志偉(Chih-Wei Wang)  查詢紙本館藏   畢業系所 統計研究所
論文名稱
(Bayesian Prediction on Longitudinal Data with Random Effects Covariance Matrix)
相關論文
★ 具Box-Cox轉換之逐步加速壽命實驗的指數推論模型★ 多元反應變數長期資料之多變量線性混合模型
★ 多重型 I 設限下串聯系統之可靠度分析與最佳化設計★ 應用累積暴露模式至單調過程之加速衰變模型
★ 串聯系統加速壽命試驗之最佳樣本數配置★ 破壞性加速衰變試驗之適合度檢定
★ 串聯系統加速壽命試驗之最佳妥協設計★ 加速破壞性衰變模型之貝氏適合度檢定
★ 加速破壞性衰變模型之最佳實驗配置★ 累積暴露模式之單調加速衰變試驗
★ 具ED過程之兩因子加速衰退試驗建模研究★ 花蓮地區地震資料改變點之貝氏模型選擇
★ 颱風降雨量之統計迴歸預測★ 花蓮地區地震資料之長時期相關性及時間-空間模型之可行性
★ 台灣地區地震資料之經驗貝氏分析★ 颱風降雨量與風速之統計預測
檔案 [Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   [檢視]  [下載]
  1. 本電子論文使用權限為同意立即開放。
  2. 已達開放權限電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。
  3. 請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。

摘要(中) 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。
摘要(英) 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.
關鍵字(中) 關鍵字(英) ★ Bayesian inference
★ Cholesky decomposition
★ Random effects
★ Mixed model
★ Markov chain Monte Carlo
★ Prediction
論文目次 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
參考文獻 Berger J.O. (1985) Statistical Decision Theory and Bayesian Analysis, 2nd Ed. Springer-Verlag, New York.
Carlin B.P. and Louis T.A. (2000) Bayes and Empirical Bayes Methods for Data Analysis, 2nd Ed. Chapman & Hall/CRC, New York.
Chib S. and Greenberg E. (1995) Understanding the Metropolis-Hastings algorithm. The American Statistician, 49, 327-335.
Chiu T.Y.M., Leonard T. and Tsui K-W. (1996) The matrix-logarithmic covariance model. Journal of the American Statistical Association, 91, 198-210.
Daniels M.J. and Kass R.E. (1999) Nonconjugate Bayesian estimation of covariance matrices and its use in hierarchical models. Journal of the American Statistical Association, 94, 1254-1263.
Daniels M.J. and Pourahmadi M. (2002) Bayesian analysis of covariance matrices and dynamic models for longitudinal data. Biometrika, 89, 553-566.
Daniels M.J. and Zhao Y.D. (2003) Modelling the random effects covariance matrix in longitudinal data. Statistics in Medicine, 22, 1631-1647.
Davidian M. and Giltinan D.M. (1995) Nonlinear Models for Repeated Measurement Data. Chapman and Hall/CRC, New York.
Diggle P.J., Liang K-Y and Zeger S.L. (1994) Analysis of Longitudinal Data. Oxford University Press, New York.
Geisser S. (1993) Predictive Inference. Chapman and Hall, London.
Graybill F. (1976) Theory and Application of the Linear Model. Wadsworth, California.
Geman S. and Geman D. (1984) Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. on Pattern Analysis and Machine Intelligence, 6, 721-741.
Gilks W.R. and Wild P. (1992) Adaptive rejection sampling for Gibbs sampling. J. Roy. Statist. Soc., Ser. C (Applied Statistics), 41, 337-348.
Hastings W.K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
Laird N.M. and Ware J.J. (1982) Random-effects models for longitudinal data. Biometrics, 38, 973-9.
Leonard T. and Hsu J.S.J. (1992) Bayesian inference for a covariance matrix. Annals of Statistics, 20, 1669-1696.
Lin X., Raz J. and Harlow S.D. (1997) Linear mixed models with heterogeneous within-cluster variances. Biometrics, 53, 910-923.
Mathews V.J. and Sicuranza G.L. (2000) Polynomial Signal Processing. John Wiley & Sons, New York.
Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H. and Teller E. (1953) Equations of state calculations by fast computing machines. J. Chemical Physics, 21, 1087-1091.
Pourahmadi M. (1999) Joint mean-covariance models with applications to longitudinal data: unconstrained parameterization. Biometrika, 86, 677-690.
Pourahmadi M. (2000) Maximum likelihood estimation of generalized linear models for multivariate normal covariance matrix. Biometrika, 87, 425-435.
Pourahmadi M. and Daniels M.J. (2002) Dynamic conditional linear mixed models for longitudinal data. Biometrics, 58, 225-231.
Rao C.R. (1973) Linear Statistical Inference and its Applications, 2nd Ed. John Wiley, New York.
Ross S.M. (2002) Simulation, 3rd Ed. Academic Press, New York.
Searle S.R., Casella G. and McCulloch C.E. (1992) Variance Components. John Wiley & Sons, New York.
Spiegelhalter D.J., Best N.G., Carlin B.P. and Linde A. (2002) Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society, Series B, 64, 583-639.
Zhang F. and Weiss R.E. (2000) Diagnosing explainable heterogeneity of variance in random effects models. Journal of Statistics, 28, 3-18.
指導教授 樊采虹(Tsai-Hung Fan) 審核日期 2007-1-25
推文 facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu   
網路書籤 Google bookmarks   del.icio.us   hemidemi   myshare   

若有論文相關問題,請聯絡國立中央大學圖書館推廣服務組 TEL:(03)422-7151轉57407,或E-mail聯絡  - 隱私權政策聲明