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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 )
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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
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指導教授 張憶壽、熊昭
(I-Shou Chang、Chao A. Hsiung)
審核日期 2003-7-3
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