In the practice of statistical modeling, it is often desirable to have an accurate predictive model. Modern data sets usually have a large number of predictors. For example, DNA microarray gene expression data usually have the characteristics of fewer observations and larger number of variables. Hence parsimony is especially an important issue. Best-subset selection is a conventional method of variable selection. Due to the large number of variables with relatively small sample size and severe collinearity among the variables, standard statistical methods for selecting relevant variables often face difficulties. / In the third part of the thesis, we propose a Bayesian stochastic search variable selection approach for multi-class classification, which can identify relevant genes by assessing sets of genes jointly. We consider a multinomial probit model with a generalized g-prior for the regression coefficients. An efficient algorithm using simulation-based MCMC methods are developed for simulating parameters from the posterior distribution. This algorithm is robust to the choice of initial value, and produces posterior probabilities of relevant genes for biological interpretation. We demonstrate the performance of the approach with two well- known gene expression profiling data: leukemia data and lymphoma data. Compared with other classification approaches, our approach selects smaller numbers of relevant genes and obtains competitive classification accuracy based on obtained results. / The last part of the thesis is about the further research, which presents a stochastic variable selection approach with different two-level hierarchical prior distributions. These priors can be used as a sparsity-enforcing mechanism to perform gene selection for classification. Using simulation-based MCMC methods for simulating parameters from the posterior distribution, an efficient algorithm can be developed and implemented. / The second part of the thesis proposes a Bayesian stochastic variable selection approach for gene selection based on a probit regression model with a generalized singular g-prior distribution for regression coefficients. Using simulation-based MCMC methods for simulating parameters from the posterior distribution, an efficient and dependable algorithm is implemented. It is also shown that this algorithm is robust to the choice of initial values, and produces posterior probabilities of related genes for biological interpretation. The performance of the proposed approach is compared with other popular methods in gene selection and classification via the well known colon cancer and leukemia data sets in microarray literature. / Yang, Aijun. / Adviser: Xin-Yuan Song. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 89-98). / 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 Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

After the stability and sensitivity of FLOR were investigated, the application of it in the CAT environment had become the main concern. The present studies found that both the test length and the number of exposed items affect the final value of FLOR. In the fixed length CAT, the FLOR has a much stronger sensitivity than lz and CUSUM in detecting item pre-knowledge. The sensitivity of FLOR in the fixed length CAT was the same as that in the fixed length fixed items test. If the test length could vary, the sensitivity of FLOR in CAT would be slightly weakened. The Adjusted FLOR index could increase the sensitivity. Concerning about the effect of ability on the sensitivity of FLOR in CAT, it was found that the abilities of the test takers in CAT did not affect the sensitivity of FLOR and Adjusted FLOR. / Item response theory is a modern test theory. It focuses on the performance of each item. Under this framework, the performance of test takers on a test item can be predicted by a set of abilities. The relationship between the test takers' item performances and the set of abilities underlying item performances can be described by a monotonically increasing function called an item characteristic curve. Due to various personal reasons, the performances of the test takers may depart from the response patterns predicted by the underlying test model. In order to calculate the extent of departure of these aberrant response patterns, a number of methods have been developed under the theme "person-fit statistics". The degree of aberration is calculated as an index called person-fit index. Inside the computerized adaptive testing (CAT), test takers with different abilities will answer different numbers of questions and the difficulties of the items administered to them are usually clustered at the abilities of the test takers. Due to this reason, the application of person-fit indices in the computerized adaptive testing environment to measure misfit is difficult. / The present study also found that FLOR has a much superior sensitivity over other indices in detecting item pre-knowledge. Concerning about the sensitivity over different abilities of test takers, it was found that the sensitivity of FLOR was the highest among low ability test takers and the weakest among strong ability test takers in the fixed length and fixed items tests. However, the sensitivities of FLOR became the same among different abilities of test takers if items with difficulties matching their abilities were used in the tests. The number of beneficiaries among the test takers did not affect the sensitivity of FLOR. Moreover, in a simulation to test the differentiating power of FLOR, it was found that FLOR could differentiate item pre-knowledge from other reasons of personal misfits (test anxiety, player, random response and challenger) effectively. / The present study assessed the stability of FLOR over other variables, which were unrelated to item pre-knowledge. It found that FLOR was stable over the discrimination and difficulty parameters of test items. It was also stable over positions of the exposed items in the test and the initial assignment of prior probability of item pre-knowledge. However, the asymptotes (guessing factor) and the probabilities of item exposure did affect the final values of FLOR seriously. / The present study used the hf plot to access the sensitivity of the person-fit indices. hf plot is a plot of hit rate against false alarm rate. For a higher hit rate, usually a higher false alarm rate is followed. hf plot provides a good tools for comparison between indices by inspection of the speed of rise of the curves. A sensitive index should give a faster rise of the curve. In this study, sensitivity of an index was defined as the speed of rise of the hf plot, which is represented by a parameter hftau estimated from the data obtained from hf plot. / When the frequent accesses to the item bank has become feasible, test takers may memorize blocks of test items and share these items with future test takers. Individuals with prior knowledge of some items may use that information to get high scores, in the sense that their test scores have been artificially inflated. FLOR is an index of posterior log-odds ratio used for detecting the use of item pre-knowledge. It can be applied both in the fixed item, fixed length test and the CAT environment. It is a model-based index in which aberrant models are defined in the situation of item pre-knowledge. FLOR describes the likelihood that a response pattern arises from the aberrant models. / Hui Hing-fai. / Adviser: Kit-tai Hau. / Source: Dissertation Abstracts International, Volume: 70-09, Section: A, page: . / Thesis (Ed.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 108-111). / 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. / Abstracts in English and Chinese. / School code: 1307.

by Jian-Qing Shi. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 118-123). / Chapter Chapter 1. --- Introduction and overview --- p.1 / Chapter Chapter 2. --- General methodology --- p.8 / Chapter Chapter 3. --- A Bayesian approach to confirmatory factor analysis --- p.16 / Chapter 3.1 --- Confirmatory factor analysis model and its prior --- p.16 / Chapter 3.2 --- The algorithm of data augmentation --- p.19 / Chapter 3.2.1 --- Data augmentation and one-run method --- p.19 / Chapter 3.2.2 --- Rao-Blackwellized estimation --- p.22 / Chapter 3.3 --- Asymptotic properties --- p.28 / Chapter 3.3.1 --- Asymptotic normality and posterior covariance matrix --- p.28 / Chapter 3.3.2 --- Goodness-of-fit statistic --- p.31 / Chapter Chapter 4. --- Bayesian inference for structural equation models --- p.34 / Chapter 4.1 --- LISREL Model and prior information --- p.34 / Chapter 4.2 --- Algorithm and conditional distributions --- p.38 / Chapter 4.2.1 --- Data augmentation algorithm --- p.38 / Chapter 4.2.2 --- Conditional distributions --- p.39 / Chapter 4.3 --- Posterior analysis --- p.44 / Chapter 4.3.1 --- Rao-Blackwellized estimation --- p.44 / Chapter 4.3.2 --- Asymptotic properties and goodness-of-fit statistic --- p.45 / Chapter 4.4 --- Simulation study --- p.47 / Chapter Chapter 5. --- A Bayesian estimation of factor score with non-standard data --- p.52 / Chapter 5.1 --- General Bayesian approach to polytomous data --- p.52 / Chapter 5.2 --- Covariance matrix of the posterior distribution --- p.61 / Chapter 5.3 --- Data augmentation --- p.65 / Chapter 5.4 --- EM algorithm --- p.68 / Chapter 5.5 --- Analysis of censored data --- p.72 / Chapter 5.5.1 --- General Bayesian approach --- p.72 / Chapter 5.5.2 --- EM algorithm --- p.76 / Chapter 5.6 --- Analysis of truncated data --- p.78 / Chapter Chapter 6. --- Structural equation model with continuous and polytomous data --- p.82 / Chapter 6.1 --- Factor analysis model with continuous and polytomous data --- p.83 / Chapter 6.1.1 --- Model and Bayesian inference --- p.83 / Chapter 6.1.2 --- Gibbs sampler algorithm --- p.85 / Chapter 6.1.3 --- Thresholds parameters --- p.89 / Chapter 6.1.4 --- Posterior analysis --- p.92 / Chapter 6.2 --- LISREL model with continuous and polytomous data --- p.94 / Chapter 6.2.1 --- LISREL model and Bayesian inference --- p.94 / Chapter 6.2.2 --- Posterior analysis --- p.101 / Chapter 6.3 --- Simulation study --- p.103 / Chapter Chapter 7. --- Further development --- p.108 / Chapter 7.1 --- More about one-run method --- p.108 / Chapter 7.2 --- Structural equation model with censored data --- p.111 / Chapter 7.3 --- Multilevel structural equation model --- p.114 / References --- p.118 / Appendix --- p.124 / Chapter A.1 --- The derivation of conditional distribution --- p.124 / Chapter A.2 --- Generate a random variate from normal density which restricted in an interval --- p.129 / Tables --- p.132 / Figures --- p.155

Oi-Ping Chiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 45-46). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Model --- p.4 / Chapter 2.1 --- General Model --- p.4 / Chapter 2.2 --- Constraint --- p.5 / Chapter 3 --- Bayesian Estimation via Gibbs Sampler --- p.7 / Chapter 3.1 --- Conditional Distributions --- p.10 / Chapter 3.2 --- Constraint --- p.15 / Chapter 3.3 --- Bayesian Estimation --- p.16 / Chapter 4 --- Model Comparison using the Bayes Factor --- p.18 / Chapter 5 --- Simulation Study --- p.22 / Chapter 6 --- Real Example --- p.27 / Chapter 6.1 --- Model Selection --- p.29 / Chapter 6.2 --- Bayesian Estimate --- p.30 / Chapter 6.3 --- Sensitivity Analysis --- p.31 / Chapter 7 --- Discussion --- p.32 / Chapter A --- p.34 / Bibliography --- p.45

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Zhang, Wei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 95-109). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Area of Machine Learning --- p.1 / Chapter 1.1.1 --- Types of Algorithms --- p.2 / Chapter 1.1.2 --- Modeling Assumptions --- p.4 / Chapter 1.2 --- Dimensionality Reduction --- p.4 / Chapter 1.3 --- Structure of the Thesis --- p.8 / Chapter 2 --- Dimensionality Reduction --- p.10 / Chapter 2.1 --- Feature Extraction --- p.11 / Chapter 2.1.1 --- Linear Feature Extraction --- p.11 / Chapter 2.1.2 --- Nonlinear Feature Extraction --- p.16 / Chapter 2.1.3 --- Sparse Feature Extraction --- p.19 / Chapter 2.1.4 --- Nonnegative Feature Extraction --- p.19 / Chapter 2.1.5 --- Incremental Feature Extraction --- p.20 / Chapter 2.2 --- Feature Selection --- p.20 / Chapter 2.2.1 --- Viewpoint of Feature Extraction --- p.21 / Chapter 2.2.2 --- Feature-Level Score --- p.22 / Chapter 2.2.3 --- Subset-Level Score --- p.22 / Chapter 3 --- Various Views of Feature Extraction --- p.24 / Chapter 3.1 --- Probabilistic Models --- p.25 / Chapter 3.2 --- Matrix Factorization --- p.26 / Chapter 3.3 --- Graph Embedding --- p.28 / Chapter 3.4 --- Manifold Learning --- p.28 / Chapter 3.5 --- Distance Metric Learning --- p.32 / Chapter 4 --- Tensor linear Laplacian discrimination --- p.34 / Chapter 4.1 --- Motivation --- p.35 / Chapter 4.2 --- Tensor Linear Laplacian Discrimination --- p.37 / Chapter 4.2.1 --- Preliminaries of Tensor Operations --- p.38 / Chapter 4.2.2 --- Discriminant Scatters --- p.38 / Chapter 4.2.3 --- Solving for Projection Matrices --- p.40 / Chapter 4.3 --- Definition of Weights --- p.44 / Chapter 4.3.1 --- Contextual Distance --- p.44 / Chapter 4.3.2 --- Tensor Coding Length --- p.45 / Chapter 4.4 --- Experimental Results --- p.47 / Chapter 4.4.1 --- Face Recognition --- p.48 / Chapter 4.4.2 --- Texture Classification --- p.50 / Chapter 4.4.3 --- Handwritten Digit Recognition --- p.52 / Chapter 4.5 --- Conclusions --- p.54 / Chapter 5 --- Semi-Supervised Semi-Riemannian Metric Map --- p.56 / Chapter 5.1 --- Introduction --- p.57 / Chapter 5.2 --- Semi-Riemannian Spaces --- p.60 / Chapter 5.3 --- Semi-Supervised Semi-Riemannian Metric Map --- p.61 / Chapter 5.3.1 --- The Discrepancy Criterion --- p.61 / Chapter 5.3.2 --- Semi-Riemannian Geometry Based Feature Extraction Framework --- p.63 / Chapter 5.3.3 --- Semi-Supervised Learning of Semi-Riemannian Metrics --- p.65 / Chapter 5.4 --- Discussion --- p.72 / Chapter 5.4.1 --- A General Framework for Semi-Supervised Dimensionality Reduction --- p.72 / Chapter 5.4.2 --- Comparison to SRDA --- p.74 / Chapter 5.4.3 --- Advantages over Semi-supervised Discriminant Analysis --- p.74 / Chapter 5.5 --- Experiments --- p.75 / Chapter 5.5.1 --- Experimental Setup --- p.76 / Chapter 5.5.2 --- Face Recognition --- p.76 / Chapter 5.5.3 --- Handwritten Digit Classification --- p.82 / Chapter 5.6 --- Conclusion --- p.84 / Chapter 6 --- Summary --- p.86 / Chapter A --- The Relationship between LDA and LLD --- p.89 / Chapter B --- Coding Length --- p.91 / Chapter C --- Connection between SRDA and ANMM --- p.92 / Chapter D --- From S3RMM to Graph-Based Approaches --- p.93 / Bibliography --- p.95

Cheng, Tsz Ho Tony. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 49-68). / Abstract also in Chinese. / ABSTRACT --- p.i / 摘要 --- p.ii / ACKNOWLEDGEMENT --- p.iii / LIST OF TABLES --- p.vi / Chapter CHAPTER 1. --- INTRODUCTION --- p.1 / What is El? --- p.2 / Controversies of El --- p.5 / Previous Research of El in the Workplace --- p.6 / Purpose of the Present Meta-Analysis --- p.7 / Specific Hypotheses Concerning El-Workplace Criterion Relations --- p.8 / El and Job Performance --- p.8 / El and Job-Related Attitudes --- p.9 / El and Leadership --- p.12 / El Models as Moderator --- p.15 / Emotional Labor Demand as Moderator --- p.16 / Gender as Moderator --- p.18 / Source of Criterion Ratings --- p.19 / Publication Bias --- p.20 / Chapter CHAPTER 2. --- METHOD --- p.21 / Literature Search --- p.21 / Inclusion Criteria --- p.21 / Coding --- p.22 / Meta-Analytic Calculation --- p.23 / Chapter CHAPTER 3. --- RESULTS --- p.26 / Descriptive Statistics of Included Samples --- p.26 / Reliability Estimates for Emotional Intelligence and Its Correlates --- p.27 / Mean Effect Analyses --- p.27 / Moderator Analyses --- p.28 / Chapter CHAPTER 4. --- DISCUSSION --- p.38 / Discussion of Key Findings --- p.38 / Main Effects of El --- p.38 / El Models --- p.39 / Emotional Labor Demand --- p.41 / Gender --- p.42 / Source of Criterion Ratings --- p.43 / Future Research --- p.44 / Conceptualizing and Measuring El --- p.44 / El at Team Level --- p.45 / Training Programs --- p.46 / Limitations --- p.46 / Concluding Remarks --- p.48 / REFERENCES --- p.49 / APPENDIX A --- p.69

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The thesis consists of three independent topics, each of which is discussed in an individual chapter. The first chapter considers a multiperiod optimal transport problem where distributions μ0, . . . , μn are prescribed and a transport corresponds to a scalar martingale X with marginals Xt ∼ μt. We introduce particular couplings called left-monotone transports; they are characterized equivalently by a no-crossing property of their support, as simultaneous optimizers for a class of bivariate transport cost functions with a Spence–Mirrlees property, and by an order-theoretic minimality property. Left-monotone transports are unique if μ0 is atomless, but not in general. In the one-period case n = 1, these transports reduce to the Left-Curtain coupling of Beiglbo ̈ck and Juillet. In the multiperiod case, the bivariate marginals for dates (0,t) are of Left-Curtain type, if and only if μ0, . . . , μn have a specific order property. The general analysis of the transport problem also gives rise to a strong duality result and a description of its polar sets. Finally, we study a variant where the intermediate marginals μ1,...,μn−1 are not prescribed. The second chapter studies the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of n-player equilibria converges to it as n → ∞. However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that mean field equilibria satisfying a transversality condition are limit points of n-player equilibria, but we also exhibit a remarkable class of mean field equilibria that are not limits, thus questioning their interpretation as “large n” equilibria. The third chapter studies the equilibrium price of an asset that is traded in continuous time between N agents who have heterogeneous beliefs about the state process underlying the asset’s payoff. We propose a tractable model where agents maximize expected returns under quadratic costs on inventories and trading rates. The unique equilibrium price is characterized by a weakly coupled system of linear parabolic equations which shows that holding and liquidity costs play dual roles. We derive the leading-order asymptotics for small transaction and holding costs which give further insight into the equilibrium and the consequences of illiquidity.

Existing methods to systematically characterize sequence-intrinsic activity of promoters are limited by relatively low throughput and the length of sequences that could be tested. Here we present Survey of Regulatory Elements (SuRE), a method to assay more than a billion DNA fragments in parallel for their ability to drive transcription autonomously. In SuRE, a plasmid library is constructed of random genomic fragments upstream of a barcode and decoded by paired-end sequencing. This library is transfected into cells and transcribed barcodes are quantified in the RNA by high-throughput sequencing. By computationally analyzing the resulting data using generalized linear models, we succeed in delineating subregions within promoters that are relevant for their activity on a genomic scale, and making accurate predictions of expression levels that can be used to inform minimal promoter reporter construct design. We also show how our approach can be extended to analyze the differential impact of single-nucleotide polymorphisms (SNPs) on gene expression.