This thesis contains two parts. The first part derives the Bayesian estimator of the parameters in a piecewise exponential Cox proportional hazard regression model, with one unknown change point for a right censored survival data. The second part surveys the applications of change point problems to various types of data, such as long-term survival data, longitudinal data and time series data. Furthermore, the proposed method is then used to analyse a real survival data. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2014. / FAU Electronic Theses and Dissertations Collection

Keywords: MCEM algorithm; Gibbs sampler; Multivariate probit model; Multi-group; BIC. / The main purpose of this paper is to develop maximum likelihood and Bayesian approach for the multivariate probit model in several populations. A Monte Carlo EM algorithm is proposed for obtaining the maximum likelihood estimates and the Gibbs sampler is used to produce the joint Bayesian estimates. To test hypotheses involving constraints among the structural parameters of MP model across groups, we use the method of Bayesian Information Criterion(BIC). The simulation study will be given to certify the accuracy of our algorithm. / Yu, Yin. / "March 2007." / Adviser: Sik Yum Lee. / Source: Dissertation Abstracts International, Volume: 68-09, Section: B, page: 6054. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 135-137). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

By the Bayesian decision theoretical view, we propose several extensions of current popular graph based methods. Several data-dependent graph construction approaches are proposed by adopting more flexible density estimators. The advantage of these approaches is that the parameters for constructing the graph can be estimated from the data. The constructed graph explores the intrinsic distribution of the data. As a result, the algorithm is more robust. It can obtain good performance constantly across different data sets. Using the flexible density models can result in directed graphs which cannot be handled by traditional graph partitioning algorithms. To tackle this problem, we propose general algorithms for graph partitioning, which can deal with both undirected and directed graphs in a unified way. / In this thesis, we establish a novel probabilistic framework for the data clustering problem from the perspective of Bayesian decision theory. The Bayesian decision theory view justifies the important questions: what is a cluster and what a clustering algorithm should optimize. / We prove that the spectral clustering (to be specific, the normalized cut) algorithm can be derived from this framework. Especially, it can be shown that the normalized cut is a nonparametric clustering method which adopts a kernel density estimator as its density model and tries to minimize the expected classification error or Bayes risk. / Chen, Mo. / Adviser: Xiaoou Tang. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 96-104). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Wai-tung Ho. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 81-83). / Chapter CHAPTER 1 --- OVERVIEW OF CONSTRAINTED ESTIMATION OF STRUCTURAL EQUATION MODEL --- p.1 / Chapter CHAPTER 2 --- MULTISAMPLE ANALYSIS OF STRUCTURAL EQUATION MODELS WITH STOCHASTIC CONSTRAINTS --- p.4 / Chapter 2.1 --- The Basic Model --- p.4 / Chapter 2.2 --- Bayesian Approach to Nuisance Parameters --- p.5 / Chapter 2.3 --- Estimation and Algorithm --- p.8 / Chapter 2.4 --- Asymptotic Properties of the Bayesian Estimate --- p.11 / Chapter CHAPTER 3 --- MULTISAMPLE ANALYSIS OF STRUCTURAL EQUATION MODELS WITH EXACT AND STOCHASTIC CONSTRAINTS --- p.17 / Chapter 3.1 --- The Basic Model --- p.17 / Chapter 3.2 --- Bayesian Approach to Nuisance Parameters and Estimation Procedures --- p.18 / Chapter 3.3 --- Asymptotic Properties of the Bayesian Estimate --- p.20 / Chapter CHAPTER 4 --- SIMULATION STUDIES AND NUMERICAL EXAMPLE --- p.24 / Chapter 4.1 --- Simulation Study for Identified Models with Stochastic Constraints --- p.24 / Chapter 4.2 --- Simulation Study for Non-identified Models with Stochastic Constraints --- p.29 / Chapter 4.3 --- Numerical Example with Exact and Stochastic Constraints --- p.32 / Chapter CHAPTER 5 --- DISCUSSION AND CONCLUSION --- p.34 / APPENDICES --- p.36 / TABLES --- p.66 / REFERENCES --- p.81

by Chi-van Lam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 71-72). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- The Model and the Bayes risk --- p.7 / Chapter § 2.1 --- The Model / Chapter § 2.2 --- The Bayes risk / Chapter Chapter 3 --- The Algorithm --- p.16 / Chapter § 3.1 --- A finite algorithm / Chapter § 3.2 --- The Number Theoretical Method for Optimization / Chapter § 3.2.1 --- NTMO / Chapter § 3.2.2 --- SNTMO / Chapter Chapter 4 --- Quadratic Loss Function --- p.26 / Chapter §4.1 --- The Bayes risk / Chapter § 4.2 --- An optimal plan / Chapter § 4.3 --- Numerical Examples / Chapter Chapter 5 --- Conclusions and Comments --- p.42 / Chapter § 5.1 --- Comparison between various plans / Chapter § 5.2 --- Sensitivity Analysis / Chapter § 5.3 --- Further Developments / Tables --- p.46 / Appendix A --- p.60 / Appendix B --- p.65 / References --- p.71

Low Kon Fan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 165-168). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgment --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview of Information Filtering --- p.1 / Chapter 1.2 --- Contributions --- p.4 / Chapter 1.3 --- Organization of this thesis --- p.6 / Chapter 2 --- Existing Approaches --- p.7 / Chapter 2.1 --- Representational issues --- p.7 / Chapter 2.1.1 --- Document Representation --- p.7 / Chapter 2.1.2 --- Feature Selection --- p.11 / Chapter 2.2 --- Traditional Approaches --- p.15 / Chapter 2.2.1 --- NewsWeeder --- p.15 / Chapter 2.2.2 --- NewT --- p.17 / Chapter 2.2.3 --- SIFT --- p.19 / Chapter 2.2.4 --- InRoute --- p.20 / Chapter 2.2.5 --- Motivation of Our Approach --- p.21 / Chapter 2.3 --- Probabilistic Approaches --- p.23 / Chapter 2.3.1 --- The Naive Bayesian Approach --- p.25 / Chapter 2.3.2 --- The Bayesian Independence Classifier Approach --- p.28 / Chapter 2.4 --- Comparison --- p.31 / Chapter 3 --- Our Bayesian Network Approach --- p.33 / Chapter 3.1 --- Backgrounds of Bayesian Networks --- p.34 / Chapter 3.2 --- Bayesian Network Induction Approach --- p.36 / Chapter 3.3 --- Automatic Construction of Bayesian Networks --- p.38 / Chapter 4 --- Automatic Feature Discretization --- p.50 / Chapter 4.1 --- Predefined Level Discretization --- p.52 / Chapter 4.2 --- Lloyd's algorithm . . > --- p.53 / Chapter 4.3 --- Class Dependence Discretization --- p.55 / Chapter 5 --- Experiments and Results --- p.59 / Chapter 5.1 --- Document Collections --- p.60 / Chapter 5.2 --- Batch Filtering Experiments --- p.63 / Chapter 5.3 --- Batch Filtering Results --- p.65 / Chapter 5.4 --- Incremental Session Filtering Experiments --- p.87 / Chapter 5.5 --- Incremental Session Filtering Results --- p.88 / Chapter 6 --- Conclusions and Future Work --- p.105 / Appendix A --- p.107 / Appendix B --- p.116 / Appendix C --- p.126 / Appendix D --- p.131 / Appendix E --- p.145

Au Siu Chun Brian. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 54-57). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Related sampling methods --- p.4 / Chapter 2.1 --- Introduction --- p.4 / Chapter 2.2 --- Gibbs sampler --- p.4 / Chapter 2.3 --- Importance sampling --- p.5 / Chapter 2.4 --- Sampling-importance resampling (SIR) --- p.7 / Chapter 2.5 --- Inverse Bayes formulae sampling (IBF sampling) --- p.10 / Chapter 3 --- Resampling weights in the SIR algorithm --- p.13 / Chapter 3.1 --- Resampling weights --- p.13 / Chapter 3.2 --- Problem in IBF sampling --- p.18 / Chapter 3.3 --- Adaptive finite mixture of distributions --- p.18 / Chapter 3.4 --- Allowing general distribution of 9 --- p.21 / Chapter 3.5 --- Examples and graphical comparison --- p.24 / Chapter 4 --- Resampling weight in Gibbs sampling --- p.32 / Chapter 4.1 --- Introduction --- p.32 / Chapter 4.2 --- Use Gibbs sampler to obtain ISF --- p.33 / Chapter 4.3 --- How many iterations? --- p.36 / Chapter 4.4 --- Applications --- p.41 / Chapter 4.4.1 --- The genetic linkage model --- p.41 / Chapter 4.4.2 --- Example --- p.43 / Chapter 4.4.3 --- The probit binary regression model --- p.44 / Chapter 5 --- Conclusion and discussion --- p.49 / Appendix A: Exact bias of the SIR --- p.52 / References --- p.54

在貝葉斯推理框架下，貝葉斯方法可以通過數據推斷複雜概率模型中的參數和結構。它被廣泛應用於多个領域。對於生物信息學問題，貝葉斯方法同樣也是一個理想的方法。本文通過介紹新的貝葉斯模型和計算方法討論並解決了兩個與模型選擇相關的生物信息學問題。 / 第一個問題是關於在DNA 序列中的模式識別的相關研究。串聯重複序列片段在DNA 序列中經常出現。它對於基因組進化和人類疾病的研究非常重要。在這一部分，本文主要討論不確定數目的同一模式的串聯重複序列彌散分佈在同一個序列中的情況。我們首先對串聯重複序列片段構建概率模型。然後利用馬爾可夫鏈蒙特卡羅算法探索後驗分佈進而推斷出串聯重複序列的重複片段的模式矩陣和位置。此外，利用RJMCMC 算法解決由不確定數目的重複片段引起的模型選擇問題。 / 另一個問題是對於生物分子的構象轉換的分析。一組生物分子的構象可被分成幾個不同的亞穩定狀態。由於生物分子的功能和構象之間的固有聯繫，構象轉變在不同的生物分子的生物過程中都扮演者非常重要的角色。一般我們從分子動力學模擬中可以得到構象轉換的數據。基於從分子動力學模擬中得到的微觀狀態水準上的構象轉換資訊，我們利用貝葉斯方法研究從微觀狀態到可變數目的亞穩定狀態的聚合問題。 / 本文通過對以上兩個問題討論闡釋貝葉斯方法在生物信息學研究的多個方面具備優勢。這包括闡述生物問題的多變性，處理噪聲和失數據，以及解決模型選擇問題。 / Bayesian approach is a powerful framework for inferring the parameters and structures of complicated probabilistic models from data. It is widely applied in many areas and also ideal for Bioinformatics problems due to their usually high complexity. In this thesis, new Bayesian models and computing methods are introduced to solve two Bioinformatics problems which are both related to model selection. / The first problem is about the repeat pattern recognition. Tandem repeats occur frequently in DNA sequences. They are important for studying genome evolution and human disease. This thesis focuses on the case that an unknown number of tandem repeat segments of the same pattern are dispersively distributed in a sequence. A probabilistic generative model is introduced for the tandem repeats. Markov chain Monte Carlo algorithms are used to explore the posterior distribution as an effort to infer both the specific pattern of the tandem repeats and the location of repeat segments. Furthermore, reversible jump Markov chain Monte Carlo algorithms are used to address the transdimensional model selection problem raised by the variable number of repeat segments. / The second part of this thesis is engaged in the conformational transitions of biomolecules. Because the function of a biological biomolecule is inherently related to its variable conformations which can be grouped into a set of metastable or long-live states, conformational transitions are important in biological processes. The 3D structure changes are generally simulated from the molecular dynamics computer simulation. Based on the conformational transitions on microstate level from molecular dynamics simulation, a Bayesian approach is developed to cluster the microstates into an uncertainty number of metastable that induces the model selection problem. / With these two problems, this thesis shows that the Bayesian approach for bioinformatics problems has its advantages in terms of taking account of the inherent uncertainty in biological data, handling noisy or missing data, and dealing with the model selection problem. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Liang, Tong. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 120-130). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Statistical Background --- p.2 / Chapter 1.3 --- Tandem Repeats --- p.4 / Chapter 1.4 --- Conformational Space --- p.5 / Chapter 1.5 --- Outlines --- p.7 / Chapter 2 --- Preliminaries --- p.9 / Chapter 2.1 --- Bayesian Inference --- p.9 / Chapter 2.2 --- Markov chain Monte Carlo --- p.10 / Chapter 2.2.1 --- Gibbs sampling --- p.11 / Chapter 2.2.2 --- Metropolis - Hastings algorithm --- p.12 / Chapter 2.2.3 --- Reversible Jump MCMC --- p.12 / Chapter 3 --- Detection of Dispersed Short Tandem Repeats Using Reversible Jump MCMC --- p.14 / Chapter 3.1 --- Background --- p.14 / Chapter 3.2 --- Generative Model --- p.17 / Chapter 3.3 --- Statistical inference --- p.18 / Chapter 3.3.1 --- Likelihood --- p.19 / Chapter 3.3.2 --- Prior Distributions --- p.19 / Chapter 3.3.3 --- Sampling from Posterior Distribution via RJMCMC --- p.20 / Chapter 3.3.4 --- Extra MCMC moves for better mixing --- p.26 / Chapter 3.3.5 --- The complete algorithm --- p.29 / Chapter 3.4 --- Experiments --- p.29 / Chapter 3.4.1 --- Evaluation and comparison of the two RJMCMC versions using synthetic data --- p.30 / Chapter 3.4.2 --- Comparison with existing methods using synthetic data --- p.33 / Chapter 3.4.3 --- Sensitivity to Priors --- p.43 / Chapter 3.4.4 --- Real data experiment --- p.45 / Chapter 3.5 --- Discussion --- p.50 / Chapter 4 --- A Probabilistic Clustering Algorithm for Conformational Changes of Biomolecules --- p.53 / Chapter 4.1 --- Introduction --- p.53 / Chapter 4.1.1 --- Molecular dynamic simulation --- p.54 / Chapter 4.1.2 --- Hierarchical Conformational Space --- p.55 / Chapter 4.1.3 --- Clustering Algorithms --- p.56 / Chapter 4.2 --- Generative Model --- p.58 / Chapter 4.2.1 --- Model 1: Vanilla Model --- p.59 / Chapter 4.2.2 --- Model 2: Zero-Inflated Model --- p.60 / Chapter 4.2.3 --- Model 3: Constrained Model --- p.61 / Chapter 4.2.4 --- Model 4: Constrained and Zero-Inflated Model --- p.61 / Chapter 4.3 --- Statistical Inference for Vanilla Model --- p.62 / Chapter 4.3.1 --- Priors --- p.62 / Chapter 4.3.2 --- Posterior distribution --- p.63 / Chapter 4.3.3 --- Collapsed Gibbs for Vanilla Model with a Fixed Number of Clusters --- p.63 / Chapter 4.3.4 --- Inference on the Number of Clusters --- p.65 / Chapter 4.3.5 --- Synthetic Data Study --- p.68 / Chapter 4.4 --- Statistical Inference for Zero-Inflated Model --- p.76 / Chapter 4.4.1 --- Method 1 --- p.78 / Chapter 4.4.2 --- Method 2 --- p.81 / Chapter 4.4.3 --- Synthetic Data Study --- p.84 / Chapter 4.5 --- Statistical Inference for Constrained Model --- p.85 / Chapter 4.5.1 --- Priors --- p.85 / Chapter 4.5.2 --- Posterior Distribution --- p.86 / Chapter 4.5.3 --- Collapsed Posterior Distribution --- p.86 / Chapter 4.5.4 --- Updating for Cluster Labels K --- p.89 / Chapter 4.5.5 --- Updating for Constrained Λ from Truncated Distribution --- p.89 / Chapter 4.5.6 --- Updating the Number of Clusters --- p.91 / Chapter 4.5.7 --- Uniform Background Parameters on Λ --- p.92 / Chapter 4.6 --- Real Data Experiments --- p.93 / Chapter 4.7 --- Discussion --- p.104 / Chapter 5 --- Conclusion and FutureWork --- p.107 / Chapter A --- Appendix --- p.109 / Chapter A.1 --- Post-processing for indel treatment --- p.109 / Chapter A.2 --- Consistency Score --- p.111 / Chapter A.3 --- A Proof for Collapsed Posterior distribution in Constrained Model in Chapter 4 --- p.111 / Chapter A.4 --- Estimated Transition Matrices for Alanine Dipeptide by Chodera et al. (2006) --- p.117 / Bibliography --- p.120

"We analyze mortality data from prostate, colon, lung, and all other types (called other cancer) to obtain age specific and age adjusted mortality rates for white males in the U.S. A related problem is to estimate the relative occurrences of these four types of cancer. We use Bayesian method because it permits a degree of smoothing which is needed to analyze data at a small area level and to assess the patterns. In the recent Atlas of the United States Mortality (1996) each type of cancer was analyzed individually. The difficulty in doing so is that there are many small areas with zero deaths. We conjecture that simultaneous analyses might help to overcome this problem, and at the same time to estimate the relative occurrences. We start with a Poisson model for the deaths, which produces a likelihood function that separates into two parts: a Poisson likelihood for the rates and a multinomial likelihood for the relative occurrences. These permit the use of a standard Poisson regression model on age as in Nandram, Sedransk and Pickle (1999), and the novelty is a multivariate logit model on the relative occurrences in which per capita income, the percent of people below poverty level, education (percent of people with four years of college) and two criteria pollutants, EPAPM25 and EPASO2, are used as covariates. We fitted the models using Markov chain Monte Carlo methods. We used one of the models to present maps of occurrences and rates for the four types. An alternative model did not work well because it provides the same pattern by age and disease. We found that while EPAPM25 has a negative effect on the occurrences, EPASO2 has a positive effect. Also, we found some interesting patterns associated with the geographical variations of mortality rates and the relative occurrences of the four cancer types."

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