伯氏先驗分布在貝氏存活分析
與貝氏遞升迴歸的應用

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：148

、訪客IP：18.221.141.44

姓名

吳裕振(Yuh-Jenn Wu) 查詢紙本館藏

畢業系所

數學系

論文名稱

伯氏先驗分布在貝氏存活分析與貝氏遞升迴歸的應用
(Application of Bernstein Prior inBayesian Isotonic Regression )

相關論文

★ 用Pfam-A建議BLAST之計分表(Scoring Matrix)與空格罰分(Gap Penality)	★ Motif長度未知之貝氏多重序列比對方法
★ 現狀家庭數據在相關伽瑪致病傾向模型之無母數估計	★ 利用兄弟數據之多點遺傳連鎖分析方法
★ 半母數混合模型估計的一致性及其應用	★ 隨機右設限數據之風險率的貝氏估計方法
★ 利用Bernstein多項式來研究二元迴歸	★ 從傳染病家庭資料估計與時間相關的傳佈參數
★ 連續型變數之記數過程在傳染病資料上之應用	★ 數據依賴誤差之階梯函數迴歸的貝氏方法
★ 由伯氏多項式對形狀限制的回歸函數定義最大概似估計量

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]

本電子論文使用權限為同意立即開放。
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。
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(英)

Summary I
Bayesian survival analysis of right-censored survival data is studied using priors on Bern-
strin polynomials and Markov chain Monte Carlo methods. These priors easily take into
consideration geometric information like convexity or initial guess on the cumulative hazard functions. The support of these priors contains only smooth functions. Certain frequestist asymptotic properties of the posterior distribution are established. Simulation studies indi-cate that these Bayes methods are quite satisfactory.
Summary II
Bayesian isotonic regressions are studied using priors on Bernstein polynomials and
Markov chain Monte Carlo methods. These priors are °exible and have support the space of bounded, increasing, and continuous functions satisfying certain geometric properties, such as being convex or sigmoidal. As an application, a Baysian isotonic and sigmoidal regression model is successfully employed to conduct data normalization in cDNA microarray exper-iments with DNA control sequences, where calibration curves relating °uorescence signal intensities to gene expressional levels are studied as regression functions.

關鍵字(中)

★ 貝氏存活分析
★ 伯氏先驗分布
★ 貝氏遞升迴歸

關鍵字(英)

★ Bayesian Isotonic Regression
★ Bernstein Prior

論文目次

Part I
Bayesian Survival Analysis Using Bernstein Polynomials
Summary 2
1. Introduction 3
2. The Model 5
3. Asymptotic behavior when n is truncated 10
4. Inference with Shape Based Prior 16
5. Inference with Bernstein-Dirichlet Prior 18
6. Simulation Studies 19
7. Discussion 21
Appendix 23
References 25
Figures 27
Part II
Bayesian Isotonic Regression Using Bernstein Polynomials, with Application to
Microarray
Summary 28
1. Introduction 29
2. The Model 32
3. Bayesian Inference 35
3.1 Algorithm 36
4. Application to Microarray Data Normalization 36
4.1 Algorithm 38
4.2 The Calibration Curve 38
5. Discussion 39
6. References 42

參考文獻

References
Altomare, F. and Campiti, M. (1994). Korovkin-type Approximation Theory and its Appli-
cation. W. de Gruyter, Berlin.
Andersen, P. K., Borgan, O., Gill, R. D., and Keiding, M. (1993). Statistical Model Based
on Counting Processes. Springer-Verlag, New York.
Arjas, E. and Gasbarra, D. (1994). Nonparametric Bayesian inference from right censored
survival data using the Gibbs sampler. Statistica Sinica 4, 505-524.
Berk, R. H. (1966). Limiting behavior of posterior distributions when the model is incorrect.
Ann. Math. Statist. 37, 51-58.
Bunke, O. and Milhaud, X. (1998). Asymptotic behavior of Bayes estimates under possibly
incorrect models. Ann. Statist. 26, 617-644.
Chang, I. S., Wen, C. C., Lin, C. Y., Wu, Y. J., Yang, C. C., Jiang, S. S., Juang J. L., and
Hsiung, C. A. (2003). Bayesian isotonic regression using Bernstein polynomials, with
application to microarray data. (Preprint).
Devroye, L. and GyÄor¯, L. (1984). Nonparametric Density Estimation the L1 View. John
Wiley & Sons, New York.
Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival Analysis.
Wiley-Interscience.
Green, P. G. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian
model determination. Biometrika 82, 711-732.
Gammerman, D. (1991). Dynamic Bayesian models for survival data. Applied Statist. 40,
63-79.
Ibrahim, J. G., Chen, M. H. and Sinha D. (2001). Bayesian Survival Analysis. Springer-
Verlag, New York.
25
Kalb°eisch, J. D. and Prentice, R. L. (2002). The Statistical Analysis of Failure Time Data.
2ed. John Wiley & Sons.
McKeague, I. W. and Tighiouart, M. (2000). Bayesian estimators for conditional hazard
functions. Biometrics 56, 1007-1015.
McKeague, I. W. and Tighiouart, M. (2002). Nonparametric Bayes estimators for hazard
functions based on right censored data. Tamkang Journal of Mathematics 33, 173-189.
Petrone, S. (1999). Random Bernstein polynomials. Scandinavian Journal of Statistics 26,
373-393.
Petrone, S. and Wasserman, L. (2002). Consistency of Bernstein polynomial posteriors.
Journal of the Royal Statistical Society 64, 79-100.
Prautzsch, H., Boehm, W., and Paluszny, M. (2002). Bezier and B-Spline Technigues.
Springer-Verlag, Berlin Heidelberg.
Robert, C. P. and Casella, G. (1999). Monte Carlo Statistical Methods. Springer-Verlag,
New York.
Sinha, D. and Dey, D. K. (1997). Semiparametric Bayesian analysis of survival data.
Journal of the American Statistical Association 92, 1195-1212.
van der Vaart, A. W. and Wellner, J. A. (1996). Weak Convergence and Empirical Pro-
cesses. Springer Verlag, New York.
van der Varrt, A.W. (1998). Asymptotic Statistics. Cambridge University Press, Cam-
bridge.
Altomare, F. and Campiti, M. (1994). Korovkin-type Approximation Theory and its Appli-
cation. Walter de Gruyter, Berlin.
Barlow, R. E., Bartholomew, D. J., Bremner, J. M., and Brunk, H. D. (1972). Statistical In-
ference Under Order Restrictions: The Theory and Application of Isotonic Regression.
Wiley, New York.
Brunk, H. D. (1955). Maximum likelihood estimates of monotone parameters. Annals of
Mathematical Statistics 26, 607-616.
Brunk, H. D. (1958). On the estimation of parameters restricted by inequalities. Annals of
Mathematical Statistics 29, 437-454.
Chang, I. S., Hsiung, C. A., Wu, Y. J., and Yang, C. C. (2003). Bayesian survival analysis
using Bernstein polynomials. (Preprint).
Chudin, E., Walker, R., Kosaka, A., Wu, S. X., Rabert, D., Chang, T. K., and Kreder
D. E. (2001). Assessment of the relationship between signal intensities and transcript
concentration for A®ymetrix GeneChip arrays. Genome Biology 3, (1): research0005.1-
0005.10.
Dudoit, S. and Yang, Y. H. (2003). Bioconductor R packages for exploratory and nor-
malization of cDNA microarray data. In G. Parmigiani, E. S. Garrett, R. A. Irizarry,
and S. L. Zeger (eds.), The Analysis of Gene Expression Data. Springer-Verlag, pp.
73-101.
Dudoit, S., Yang, Y. H., Speed, T. P., and Callow, M. J. (2002). Statistical methods for
identifying di®erentially expressed genes in replicated cDNA microarray experiments.
Statistica Sinica 12, 111-139.
Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman & Hall,
New York.
Friedman, J. and Tibshirani, R. (1984). The monotone smoothing of scatterplots. Techno-
metrics 26, 242-250.
Green, P. G. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian
model determination. Biometrika 82, 711-732.
Jiang, S. S., Huang, L. W., Liu, Y. L., Lin, S. M., Wen, C. C., Chen, W. C., Chen, P.
C., Chang, I. S., Hsiung C. A., and Juang, J. L. (2003). Genome-wide transcription
pro¯ling of Autographa Californica multiple polyhedrosis virus. (In preparation).
Lavine, M. and Mockus, A. (1995). A nonparametric Bayes method for isotonic regression.
Journal of Statistical Planning and Inference 46, 235-248.
Lee, C. I. (1996). On estimation for monotone dose-response curve. Journal of the American
Statistical Association 91, 1110-1119.
Mammen, E. (1991). Estimating a smooth monotone regression function. Annals of Statis-
tics 19, 724-740.
Mukerjee, H. (1988). Monotone nonparametric regression. Annals of Statistics 16, 741-750.
Parmigiani, G., Garrett, E. S., Irizarry, R. A., and Zeger S. L. (2003). The analysis of
gene expression data: An overview of methods and software. In G. Parmigiani, E. S.
Garrett, R. A. Irizarry, and S. L. Zeger (eds.), The Analysis of Gene Expression Data,
Springer-Verlag, pp. 1-45.
Petrone, S. (1999). Random Bernstein polynomials. Scandinavian Journal of Statistics 26,
373-393.
Petrone, S. and Wasserman, L. (2002). Consistency of Bernstein polynomial posteriors.
Journal of the Royal Statistical Society B 64, 79-100.
Prautzsch, H., Boehm, W., and Paluszny, M. (2002). Bezier and B-Spline Technigues.
Springer-Verlag, Berlin Heidelberg.
Robert, C. P. and Casella, G. (1999) Monte Carlo Statistical Methods. Springer-Verlag,
New York.
Robertson, T., Wright, F. T., and Dykstra, R. L. (1988). Order Restricted Statistical
Inference. Wiley, New York.
Silverman, B. W. (1985). Some aspects of the spline smoothing approach to nonparametric
regression curve ¯tting (with discussion). Journal of the Royal Statistical Society B
47, 1-52.
Speed T. P. (2003). Statistical Analysis of Gene Expression Microarray Data. Chapman &
Hall.
Tenbusch, A. (1997). Nonparametric curve estimation with Bernstein estimates. Metrika
45, 1-30.
Wegman, E. J. and Wright, I. W. (1983). Splines in statistics. Journal of the American
Statistical Association 78, 351-365.
Wright, I. W. and Wegman, E. J. (1980). Isotonic, convex and related splines. Annals of
Statistics 8, 1023-1035.

指導教授

張憶壽、熊昭
(I-Shou Chang、Chao A. Hsiung)

審核日期

2003-7-3

推文