by Lo Ting Shek = 複雜適應系統中的個體為本模型 / 盧庭碩. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 105-107). / Text in English; abstracts in English and Chinese. / by Lo Ting Shek = Fu za shi ying xi tong zhong de ge ti wei ben mo xing / Lu Tingshuo. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Minority game --- p.9 / Chapter 2.1 --- The model --- p.9 / Chapter 2.2 --- Review on selected work on MG --- p.13 / Chapter 2.2.1 --- Market efficiency and Phase transition --- p.13 / Chapter 2.2.2 --- Crowd effect in MG --- p.17 / Chapter 2.2.3 --- Hamming distance between strategies --- p.19 / Chapter 2.2.4 --- Statistical mechanics of systems with heterogeneous agents --- p.21 / Chapter 3 --- Theory of the minority game --- p.23 / Chapter 3.1 --- Formalism --- p.23 / Chapter 3.2 --- Discussion --- p.31 / Chapter 4 --- Evolutionary Minority Game --- p.33 / Chapter 4.1 --- Model --- p.33 / Chapter 4.2 --- Results --- p.36 / Chapter 4.3 --- Discussion --- p.38 / Chapter 5 --- Theory of the Evolutionary Minority game --- p.43 / Chapter 5.1 --- The theory of D'hulst and Rodgers [1] --- p.44 / Chapter 5.1.1 --- Discussion on the D'hulst and Rodgers's theory --- p.51 / Chapter 5.2 --- Theory of EMG [2] --- p.54 / Chapter 5.2.1 --- Formalism --- p.55 / Chapter 5.2.2 --- Results --- p.60 / Chapter 5.2.3 --- Discussion --- p.66 / Chapter 6 --- Evolutionary Minority Game with arbitrary cutoffs --- p.68 / Chapter 6.1 --- Model --- p.68 / Chapter 6.2 --- Results --- p.69 / Chapter 6.3 --- Theory --- p.76 / Chapter 6.4 --- Discussion --- p.85 / Chapter 7 --- Evolutionary minority game with heterogeneous strategy distribution --- p.88 / Chapter 7.1 --- Model --- p.89 / Chapter 7.2 --- Results --- p.90 / Chapter 7.3 --- Discussion --- p.99 / Chapter 8 --- Conclusion --- p.103

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Xin-Yuan Song. / "December 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 128-142). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

This thesis explores different aspects of a surprising field of research: the conformally invariant scaling limits of planar statistical mechanics models. The aspects developed here include the proof of convergence of certain interfaces in the critical Ising magnetization model (joint work with Hugo Duminil-Copin and Clement Hongler), a study of the near-critical behavior of the uniform spanning tree in the scaling limit (joint work with Laure Dumaz and Wendelin Werner), the construction of an interesting measure on continuous loops satisfying a certain stability property under deformation (joint work with Julien Dubedat) as well as some related algebraic considerations, and finally, notes on a paper of Sheffield, that studies a certain coupling of the scaling limits of discrete interfaces - SLE curves - together with random surfaces obtained from the Gaussian free field.

Latent variable models play an important role in psychological and educational measurement, which attempt to uncover the underlying structure of responses to test items. This thesis focuses on the development of statistical learning methods based on latent variable models, with applications to psychological and educational assessments. In that connection, the following problems are considered. The first problem arises from a key assumption in latent variable modeling, namely the local independence assumption, which states that given an individual's latent variable (vector), his/her responses to items are independent. This assumption is likely violated in practice, as many other factors, such as the item wording and question order, may exert additional influence on the item responses. Any exploratory analysis that relies on this assumption may result in choosing too many nuisance latent factors that can neither be stably estimated nor reasonably interpreted. To address this issue, a family of models is proposed that relax the local independence assumption by combining the latent factor modeling and graphical modeling. Under this framework, the latent variables capture the across-the-board dependence among the item responses, while a second graphical structure characterizes the local dependence. In addition, the number of latent factors and the sparse graphical structure are both unknown and learned from data, based on a statistically solid and computationally efficient method. The second problem is to learn the relationship between items and latent variables, a structure that is central to multidimensional measurement. In psychological and educational assessments, this relationship is typically specified by experts when items are written and is incorporated into the model without further verification after data collection. Such a non-empirical approach may lead to model misspecification and substantial lack of model fit, resulting in erroneous interpretation of assessment results. Motivated by this, I consider to learn the item - latent variable relationship based on data. It is formulated as a latent variable selection problem, for which theoretical analysis and a computationally efficient algorithm are provided.

Documenting the extent of cellular diversity is a critical step in defining the functional organization of the nervous system. In this context, we sought to develop statistical methods capable of revealing underlying cellular diversity given incomplete data sampling - a common problem in biological systems, where complete descriptions of cellular characteristics are rarely available. We devised a sparse Bayesian framework that infers cell type diversity from partial or incomplete transcription factor expression data. This framework appropriately handles estimation uncertainty, can incorporate multiple cellular characteristics, and can be used to optimize experimental design. We applied this framework to characterize a cardinal inhibitory population in the spinal cord. Animals generate movement by engaging spinal circuits that direct precise sequences of muscle contraction, but the identity and organizational logic of local interneurons that lie at the core of these circuits remain unresolved. By using our Sparse Bayesian approach, we showed that V1 interneurons, a major inhibitory population that controls motor output, fractionate into diverse subsets on the basis of the expression of nineteen transcription factors. Transcriptionally defined subsets exhibit highly structured spatial distributions with mediolateral and dorsoventral positional biases. These distinctions in settling position are largely predictive of patterns of input from sensory and motor neurons, arguing that settling position is a determinant of inhibitory microcircuit organization. Finally, we extensively validated inferred cell types by direct experimental measurement and then, extend our Bayesian framework to full transcriptome technologies. Together, these findings provide insight into the diversity and organizational logic through which inhibitory microcircuits shape motor output.

Following the recent financial crisis, financial regulators have placed a strong emphasis on reducing expectations of government support for banks, and on better managing and assessing risks in the banking system. This thesis considers three current topics in credit risk and the statistical problems that arise there. The first of these topics is expectations of government support in distressed banks. We utilize unique features of the European credit default swap market to find that market expectations of European government support for distressed banks have decreased -- an important development in the credibility of financial reforms. The second topic we treat is the estimation of covariance matrices from the perspective of market risk management. This problem arises, for example, in the central clearing of credit default swaps. We propose several specialized loss functions, and a simple but effective visualization tool to assess estimators. We find that proper regularization significantly improves the performance of dynamic covariance models in estimating portfolio variance. The third topic we consider is estimation risk in the pricing of financial products. When parameters are not known with certainty, a better informed counterparty may strategically pick mispriced products. We discuss how total estimation risk can be minimized approximately. We show how a premium for remaining estimation risk may be determined when one counterparty is better informed than the other, but a market collapse is to be avoided, using a simple example from loan pricing. We illustrate the approach with credit bureau data.

Yip Kin Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 101-104). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The Distribution of Fluctuations in Financial Data --- p.5 / Chapter 2.1 --- Empirical Statistics --- p.5 / Chapter 2.2 --- Data analyzed --- p.8 / Chapter 2.3 --- Levy Distribution --- p.10 / Chapter 2.4 --- Returns Distribution and Scaling Properties --- p.12 / Chapter 2.5 --- Volatility Clustering --- p.19 / Chapter 2.6 --- Conclusion --- p.21 / Chapter 3 --- Models of Herd behaviour in Financial Markets --- p.22 / Chapter 3.1 --- Cont and Bouchaud's model --- p.22 / Chapter 3.2 --- The Model of Egiuluz and Zimmerman --- p.24 / Chapter 3.3 --- EZ Model with Size-Dependent Dissociation Rates --- p.28 / Chapter 3.4 --- Democratic and Dictatorship Self-Organized Model --- p.31 / Chapter 3.5 --- Effect of Size-Dependent Fragmentation and Coagulation Prob- abilities --- p.33 / Chapter 3.6 --- Extensions of EZ model --- p.35 / Chapter 3.7 --- Conclusion --- p.39 / Chapter 4 --- Review on the Minority Game(MG) --- p.42 / Chapter 4.1 --- The Model and Results --- p.42 / Chapter 4.2 --- Crowd-anticrowd Theory and Phase Transition --- p.46 / Chapter 4.3 --- Market Efficiency --- p.48 / Chapter 5 --- MG with biased strategy pool --- p.52 / Chapter 5.1 --- The Model --- p.53 / Chapter 5.2 --- Numerical Results and Discussion --- p.53 / Chapter 5.3 --- Theory: MG with Biased Strategy Pool --- p.61 / Chapter 5.4 --- Conclusion --- p.69 / Chapter 6 --- MG with Randomly Participating Agents --- p.71 / Chapter 6.1 --- The Model with One RPA --- p.71 / Chapter 6.2 --- Results for q = 0.5 --- p.72 / Chapter 6.3 --- Inefficiency and Success Rate --- p.76 / Chapter 6.4 --- Results for q ≠ 0.5 --- p.82 / Chapter 6.5 --- Many RPAs --- p.85 / Chapter 6.6 --- Conclusion --- p.86 / Chapter 7 --- A Model on Coupled Minority Games --- p.88 / Chapter 7.1 --- The Model --- p.89 / Chapter 7.2 --- Results and Discussion。 --- p.90 / Chapter 7.3 --- Conclusion --- p.95 / Chapter 8 --- Conclusion --- p.97 / Bibliography --- p.101 / Chapter A --- Solving Cluster Size distribution in EZ model --- p.105

行为学、社会学、心理学和医药学方面，结构方程模型(SEMs) 是研究有关潜在变量最常用的模型。这篇论文的目的是研究基本和高级结构方程模型的贝叶斯诊断，本文研究的结构方程模型包括非线性纺构方程模型、变换结构方程模型、二层结构方程模型和混合结构方程模型。基于对数贝叶斯因子的一阶与二阶局部影响测度是本文进行贝贝叶斯诊断的基础。局部影响测度的计算和模型参数估计是利用了蒙特卡洛(MCMC) 和扩展数据的方法。对比传统的基于极大似然的诊断，本文提出的贝叶斯诊断方法不仅能检测异常点或者影响点，而且可以诊断模型假设和先验设定的敏感性。 这些是通过对数据、模型假设和先验设定进行不同的扰动获得的 本文用大量的模拟实验来说明所提出的贝叶斯诊断方法的作用。 本文基于不同类型的结构方程模型，应用所提出的贝叶斯诊断方法于一些实际数据。 / In the behavioral, social, psychological, and medical sciences, the most widely used models in assessing latent variables are structural equation models (SEMs). This thesis aims to develop Bayesian diagnostic procedures for basic and advanced SEMs such as nonlinear SEMs, transformation SEMs, two-level SEMs, and mixture SEMs. The first- and second-order local inference measures with the objective functions defined based on the logarithm of Bayes factor are proposed to perform the Bayesian diagnostics. Markov chain Monte Carlo (MCMC) methods, along with data augmentation, are developed to compute the local influence measures and to estimate unknown model parameters. Compared with conventional maximum likelihood-based diagnostic procedures, the proposed Bayesian diagnostic approach can not only detect outliers or influential points in the observed data, but also conduct model comparison and sensitivity analysis by perturbing the data, sampling distributions, and the prior distributions of model parameters via a variety of perturbations. The empirical performances of the proposed Bayesian diagnostic procedures are revealed through extensive simulation studies. Several real-life data sets are used to illustrate the application of our proposed methodology in the context of different SEMs. / Detailed summary in vernacular field only. / Chen, Ji. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 130-135). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Structural equation models --- p.1 / Chapter 1.2 --- Bayesian diagnostics --- p.3 / Chapter 1.2.1 --- The first and second order local influence measures --- p.5 / Chapter 1.2.2 --- A simple example --- p.9 / Chapter 2 --- Bayesian diagnostics of nonlinear SEMs --- p.15 / Chapter 2.1 --- Model description --- p.16 / Chapter 2.2 --- Bayesian estimation and local inference of nonlinear SEMs --- p.17 / Chapter 2.3 --- Simulation study --- p.24 / Chapter 2.3.1 --- Simulation study 1 --- p.24 / Chapter 2.3.2 --- Simulation study 2 --- p.25 / Chapter 2.3.3 --- Simulation study 3 --- p.27 / Chapter 2.4 --- Application: A study of kidney disease for type 2 diabetic patients --- p.29 / Chapter 3 --- Bayesian diagnostics of transformation SEMs --- p.40 / Chapter 3.1 --- Model description --- p.41 / Chapter 3.2 --- Bayesian estimation and local inference of the transformation SEMs --- p.44 / Chapter 3.3 --- Simulation study --- p.54 / Chapter 3.3.1 --- Simulation study 1 --- p.54 / Chapter 3.3.2 --- Simulation study 2 --- p.56 / Chapter 3.4 --- Application: A study on the risk factors of osteoporotic fracture in older people --- p.58 / Chapter 4 --- Bayesian diagnostics of two-level SEMs --- p.73 / Chapter 4.1 --- Model description --- p.74 / Chapter 4.2 --- Bayesian estimation and local inference of two-level SEMs --- p.75 / Chapter 4.3 --- Simulation study --- p.88 / Chapter 4.4 --- Application: A study of AIDS data --- p.91 / Chapter 5 --- Bayesian diagnostics of mixture SEMs --- p.106 / Chapter 5.1 --- Model description --- p.107 / Chapter 5.2 --- Bayesian estimation and local inference ofmixture SEMs --- p.108 / Chapter 5.3 --- Simulation study --- p.116 / Chapter 5.3.1 --- Simulation study 1 --- p.116 / Chapter 5.3.2 --- Simulation study 2 --- p.118 / Chapter 6 --- Conclusion --- p.126 / Bibliography --- p.130 / Chapter A --- Proof of Theorem 1.1 and 1.2 --- p.136 / Chapter B --- Full conditional distributions of the nonlinear SEM --- p.138 / Chapter C --- Full conditional distributions of the transformation SEM --- p.141 / Chapter D --- Full conditional distributions of the two-level SEM --- p.144 / Chapter E --- AIDS preventative intervention data --- p.150 / Chapter F --- Permutation sampler in the mixture SEM --- p.152 / Chapter G --- Full conditional distributions of the mixture SEM --- p.153

Leung Shek-hay. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 53-55). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Finite Mixtures of Structural Equation Model --- p.4 / Chapter Chapter 3 --- Bayesian Approach --- p.7 / Chapter Chapter 4 --- Two-stage Approach --- p.16 / Chapter Chapter 5 --- Simualtion Study --- p.22 / Chapter 5.1 --- Performance of the Two Approaches --- p.22 / Chapter 5.2 --- Influence of Prior Information of the Two Approaches --- p.26 / Chapter 5.3 --- Influence of the Component Probability to the Two Approaches --- p.28 / Chapter 5.4 --- Performance of the Two Approaches when the Components are not well-separated --- p.29 / Chapter Chapter 6 --- A Real Data Analysis --- p.31 / Chapter Chapter 7 --- Conclusion and Discussion --- p.35 / Appendix A Derviation of the Conditional Distribution --- p.37 / Appendix B Manifest Variables in the ICPSR Example --- p.39 / Appendix C A Sample LISREL Program for a Classified Group in the Simualtion Study --- p.40 / Appendix D A Sample LISREL Program for a Classified Group in the ICPSR Example --- p.41 / Tables 1-9 --- p.42 / Figures 1-2 --- p.51 / References --- p.53