Selecting an appropriate model is a crucial issue for applying structural equation models (SEMs) in real applications. Due to the model complexity, however, it is quite challenging to perform model selection on semiparametric SEMs with functional structural equations. In this thesis, we propose a modified Bayesian adaptive group Lasso procedure to perform model selection and estimation for semiparametric SEMs. By considering a novel formulation of basis expansions to approximate the unknown functions with certain penalties imposed, we are able to introduce a partial linear structure that combines the advantages of linear and nonparametric formulations for structural equations. The nonlinear, linear, or none structures in structural equations can be automatically detected with the proposed method. In addition, the group Lasso with adaptive penalties not only largely alleviates the model selection difficulties caused by the group effects and correlations introduced by basis expansions of latent variables, but also reduces the bias of traditional Lasso procedures. Simulation studies demonstrate that the proposed methodology performs satisfactorily. The proposed method is applied to analyze a real data set of diabetic kidney disease, which provides us some meaningful insights. / 在结构方程模型的实际应用中，选择一个合适的模型是一个核心问题。但是由于模型的复杂性，对于含有函数型结构的半参数结构方程模型进行模型选择十分困难。在本文中，我们提出了一种新的贝叶斯自适应群Lasso，并应用它来对半参数结构方程模型同时进行参数估计和模型选择。我们在非参数结构方程模型中引入了部分线性结构，并通过一种新的基底函数展开来近似结构方程里的未知函数。这种结构同时具备了线性模型和非参数模型的优势。本文的方法可以自动识别半参数结构方程模型里面的非线性和线性结构，并筛除不重要的变量。这种带有自适应惩罚的群Lasso不仅减小了传统Lasso方法在估计参数时产生的偏差，而且解决了由潜变量的基底表示导致的组效应和相关性引起的模型选择的困难。由模拟实验的结果可以看出本文提出的方法十分有效。我们还应用所提出的方法分析了一组关于糖尿病型肾病的数据，并得到了一些有意义的结果。 / Feng, Xiangnan. / Thesis M.Phil. Chinese University of Hong Kong 2014. / Includes bibliographical references (leaves 51-56). / Abstracts also in Chinese. / Title from PDF title page (viewed on 18, October, 2016). / Detailed summary in vernacular field only.

by Chan Kam Wai Clifford. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 105-108). / Text in English; abstracts in English and Chinese. / by Chan Kam Wai Clifford. / Abstract --- p.i / Acknowledgements --- p.iii / Contents --- p.iv / List of Figures --- p.vii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Motivations of the Project --- p.1 / Chapter 1.2 --- Historical Background --- p.1 / Chapter 1.3 --- Objective and Outline of Thesis --- p.3 / Chapter Chapter 2. --- Reviews on One-dimensional Dynamical Cavity --- p.4 / Chapter 2.1 --- Formalism --- p.4 / Chapter 2.2 --- Methods of Solution --- p.6 / Chapter 2.2.1 --- Phase Construction (R function) --- p.6 / Chapter 2.2.2 --- Instantaneous Mode Expansion --- p.12 / Chapter 2.2.3 --- Transformation Method --- p.15 / Chapter 2.3 --- Numerical Results --- p.15 / Chapter 2.3.1 --- Some Results using R function --- p.16 / Chapter 2.3.2 --- Some Results using Instantaneous Mode Decomposition --- p.24 / Chapter 2.3.3 --- Remarks on the Numerical Scheme used in Transformation Method --- p.28 / Chapter 2.3.4 --- "Comparisons of Results obtained by Phase Construction, In- stantaneous Mode Decomposition and Transformation" --- p.28 / Chapter 2.4 --- Conclusion --- p.30 / Chapter Chapter 3. --- Fixed-point Analysis for the One-dimensional Cavity --- p.31 / Chapter 3.1 --- Introduction --- p.31 / Chapter 3.2 --- What are the fixed-points? --- p.32 / Chapter 3.3 --- Characteristics of Fixed-points --- p.36 / Chapter 3.4 --- Fixed-points and Geometric Resonance --- p.39 / Chapter Chapter 4. --- Electromagnetic Field in an Undulating Spherical Cavity --- p.44 / Chapter 4.1 --- Classical Electromagnetic field theory --- p.44 / Chapter 4.2 --- Boundary Conditions --- p.46 / Chapter 4.3 --- The Motion of Cavity Surface --- p.47 / Chapter Chapter 5. --- Methods of Solution and Results to the Spherical Cavity --- p.48 / Chapter 5.1 --- Introduction --- p.48 / Chapter 5.2 --- Mode Decomposition and Transformation Method revisited --- p.49 / Chapter 5.2.1 --- Mode Decomposition --- p.49 / Chapter 5.2.2 --- Transformation Method --- p.50 / Chapter 5.2.3 --- Remarks on the use of Instantaneous Mode Expansion and Transformation Method --- p.51 / Chapter 5.3 --- The Ge(z) function --- p.52 / Chapter 5.3.1 --- The Ge(z) function as a solution of the scalar wave equation --- p.52 / Chapter 5.3.2 --- Numerical Results --- p.54 / Chapter 5.4 --- The Me(z) function --- p.60 / Chapter 5.4.1 --- Formalism --- p.60 / Chapter 5.4.2 --- Comparison of Me(z) with Ge(z) --- p.62 / Chapter 5.4.3 --- Numerical Results --- p.63 / Chapter 5.5 --- Conclusions and Discussions --- p.93 / Chapter 5.5.1 --- Geometric Resonances --- p.93 / Chapter 5.5.2 --- Harmonic Resonances --- p.94 / Chapter Chapter 6. --- Conclusion --- p.95 / Appendix A. Electromagnetic Field in Spherical Cavity --- p.97 / Chapter A.1 --- Field Strength --- p.97 / Chapter A.2 --- Field Energy --- p.98 / "Appendix B. Construction of Ψe(r,t) by G(z)" --- p.100 / Appendix C. The Arbitrary Part GH(z) of Ψe(r，t) --- p.103 / Bibliography --- p.105

by Yuen Wai Ching. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 54-55). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Group Analysis --- p.9 / Chapter 2.1 --- Groups and Differential Equations --- p.9 / Chapter 2.2 --- Prolongation --- p.11 / Chapter 2.3 --- The Prolongation Formula --- p.14 / Chapter 3 --- Symmetry Group For the Eikonal Equation --- p.17 / Chapter 4 --- An Optimal System For the Eikonal Equation --- p.25 / Chapter 5 --- Group Invariant Solutions --- p.33 / Chapter 5.1 --- Straight Lines --- p.33 / Chapter 5.2 --- Stationary Solutions --- p.33 / Chapter 5.3 --- Traveling Waves --- p.34 / Chapter 5.4 --- Circles --- p.37 / Chapter 5.5 --- Spirals --- p.38 / Chapter 6 --- Appendix --- p.50 / A Group Analysis for some Geometric Evolution Equations --- p.4 / Bibliography

Fragmentation processes describe phenomena of random splitting, with possibly infinite activity, according to certain rules that give rise to a close relation of these processes to branching processes and L´evy processes. In this thesis we study some asymptotic properties of fragmentation processes. More specifically, we prove certain strong laws of large numbers for self–similar fragmentations and we deal with the existence and uniqueness of solutions ofthe one–sided FKPP travelling wave equation for homogenous fragmentation processes. In addition to being concerned with standard fragmentation processes we also consider fragmentation processes with immigration, fragmentations stopped at a stopping line as well as killed fragmentation processes.

"In this dissertation we study the so-called “city effect” problem. This effect occurs when earthquakes strike large cities. In earlier studies, seismic wave propagation was evaluated in a separate step and then impacts on man made structures above ground were calculated. The 1985 Michoacan earthquake in Mexico City led Wirgin and Bard (1996) to hypothesize that city buildings may collectively affect the ground motion during an earthquake. Ghergu and Ionescu (2009) proposed a model of this phenomenon and a solution algorithm. Our contribution is to extend their work and to provide a mathematical analysis for proving the existence of preferred frequencies coupling vibrations of buildings to underground seismic waves. Given the geometry and the specific physical constants of an idealized two dimensional city, Ghergu and Ionescu computed a frequency that will couple vibrating buildings to underground seismic waves. This frequency was obtained by increasing the number of buildings at the expense of solving larger and larger systems. Our idea is to use a periodic Green's function and perform computations on a single period. That allows for much faster computations, and makes it possible to consider more complex geometries within a single period. We provide a rather in depth and proof based account of different formulations for the periodic Green's function that we need. We show that they are indeed fundamental solutions to the Helmholtz operator and we analyze their convergence rate. Finally, we give a mathematical proof of existence of preferred frequencies coupling vibrations of buildings to underground seismic waves."

This paper introduces a method to determine the pressure in a fixed thickness, smooth, periodic domain; namely a lead-over-pleat cartridge filter. Finding the pressure within the domain requires the numerical solution of Laplace's equation, the first step of which is approximating, by interpolation, the curved portions of the filter to a circle in the xy plane.A conformal map is then applied to the filter, transforming the region into a rectangle in the uv plane. A finite difference method is introduced to numerically solve Laplace's equation in the rectangular domain. There are currently methods in existence to solve partial differential equations on non- regular domains. In a method employed by Monchmeyer and Muller, a scheme is used to transform from cartesian to spherical polar coordinates. Monchmeyer and Muller stress that for non-linear domains, extrapolation of existing cartesian difference schemes may produce incorrect solutions, and therefore, a volume centered discretization is used. A difference scheme is then derived that relies on mean values. This method has second order accuracy.(Rosenfeld,Moshe, Kwak, Dochan, 1989) The method introduced in this paper is based on a 7-point stencil which takes into account the unequal spacing of the points. From all neighboring pairs, a linear system of equations is constructed, which takes into account the periodic domain.This method is solved by standard iterative methods. The solution is then mapped back to the original domain, with second order accuracy. The method is then tested to obtain a solution to a domain which satisfies $y=sin(x)$ at the center, a shape similar to that of a lead-over-pleat cartridge filter. As a result, a model for the pressure distribution within the filter is obtained.

Dans cette thèse, nous étudions un problème de contrôle et un problème inverse pour les équationsde la chaleur. Notre premier travail concerne la contrôlabilité à zéro pour une équation de la chaleur semi-linéaire. Il est à noter que sans contrôle, la solution est instable et il y aura en général explosion de la solution en un temps fini. Ici, nous proposons un résultat positif de contrôlabilité à zéro sous une hypothèse quantifiée de petitesse sur la donnée initiale. La nouveauté réside en la construction de ce contrôle pour amener la solution à l’état d’équilibre.Notre second travail aborde l’équation de la chaleur rétrograde dans un domaine borné et sous la condition de Dirichlet. Nous nous intéressons à la question suivante: peut-on reconstruire la donnée initiale à partir d’une observation de la solution restreinte à un sous-domaine et à un temps donné? Ce problème est connu pour être mal-posé. Ici, les deux principales méthodes proposées sont: une approche de filtrage des hautes fréquences et une minimisation à la Tikhonov. A chaque fois, nous reconstruisons de manière approchée la solution et quantifions l’erreur d’approximation / My thesis focuses on two main problems in studying the heat equation: Control problem and Inverseproblem.Our first concern is the null controllability of a semilinear heat equation which, if not controlled, can blow up infinite time. Roughly speaking, it consists in analyzing whether the solution of a semilinear heat equation, underthe Dirichlet boundary condition, can be driven to zero by means of a control applied on a subdomain in whichthe equation evolves. Under an assumption on the smallness of the initial data, such control function is builtup. The novelty of our method is computing the control function in a constructive way. Furthermore, anotherachievement of our method is providing a quantitative estimate for the smallness of the size of the initial datawith respect to the control time that ensures the null controllability property.Our second issue is the local backward problem for a linear heat equation. We study here the followingquestion: Can we recover the source of a linear heat equation, under the Dirichlet boundary condition, from theobservation on a subdomain at some time later? This inverse problem is well-known to be an ill-posed problem,i.e their solution (if exists) is unstable with respect to data perturbations. Here, we tackle this problem bytwo different regularization methods: The filtering method and The Tikhonov method. In both methods, thereconstruction formula of the approximate solution is explicitly given. Moreover, we also provide the errorestimate between the exact solution and the regularized one.

Ce travail de thèse a pour but d'étudier des écoulements non stationnaires de fluides incompressibles Newtoniens et non isothermes. Le problème est décrit par les lois de conservation de la masse, de la quantité de mouvement et de l'énergie. Nous nous intéressons au couplage entre le système de Navier-Stokes et l’équation de la chaleur hyperbolique (le résultat de la combinaison entre la loi de conservation d'énergie et la loi de Cattaneo). Cette dernière est une modification de la loi de Fourier utilisée habituellement, elle permet de surmonter « le paradoxe de la chaleur » et d'obtenir une description plus précise de la propagation de la chaleur. Le système couplé est un problème hyperbolique-parabolique dont la viscosité dépend de la température, alors que la capacité thermique et le terme de dissipation dépendent de la vitesse. Afin d’obtenir un résultat d'existence de solutions du problème couplé, nous démontrons d'abord l'existence et l'unicité de la solution du problème hyperbolique puis nous introduisons une discrétisation en temps et nous étudions la convergence des solutions approchées vers celles du problème original. Dans un deuxième temps nous étudions l'existence et l'unicité de la solution du système de Navier-Stokes muni des conditions aux limites de type Tresca puis de type Coulomb en dimension 2 et 3. Dans le chapitre 3, nous proposons une discrétisation en temps du problème d'écoulement dans le cas de la condition au limite de type Tresca et nous établissons la convergence des solutions approchées. Le dernier chapitre de ce mémoire est consacré à l'étude du problème couplé dans le cas de conditions aux limites de type Tresca. L'existence d'une solution est obtenue par un argument théorique de point fixe en dimension 2 et également par une méthode de discrétisation en temps qui conduit à résoudre sur chaque sous intervalle de temps un problème découplé pour la vitesse et la pression d'une part et la température d'autre part / The main objective of this thesis is to study nonstationary flows of incompressible Newtonian and non isothermal fluids. The problem is described by the laws of conservation of mass, momentum and energy. We consider the coupling between the Navier-Stokes system and the hyperbolic heat equation (the result of combination between the law of conservation of energy and the Cattaneo’s law). This one is a modification of the commonly used Fourier's law, it overcomes "the heat paradox" and gives a more accurate description of heat propagation. The coupled system is an hyperbolic-parabolic problem where the viscosity depends on the temperature but the thermal capacity and the dissipative term depend on the velocity. To obtain an existence result for the coupled system, we first prove the existence and uniqueness of the solution of the hyperbolic problem then we introduce a time discretization and we study the convergence of the approximate solutions to those of the original problem. In the second chapter, we study the existence and uniqueness of the solution of Navier-Stokes system with Tresca or Coulomb boundary conditions in dimension 2 and 3. In the third chapter, we propose a time discretization of the flow problem in the case of Tresca boundary conditions and we establish the convergence of the approximate solutions. The last chapter is devoted to the study of the coupled problem in the case of Tresca free boundary conditions. The existence of a solution is obtained by a theoretical argument (fixed-point theorem) in dimension 2 and also by a method of time discretization leading, on each time subinterval, to a decoupled problem for the velocity and pressure of a hand and the temperature of the other hand

Structural equation models (SEMs) are commonly used in behavioral, educational, medical, and social sciences. Lots of software, such as EQS, LISREL, MPlus, and WinBUGS, can be used for the analysis of SEMs. Also many methods have been developed to analyze SEMs. One popular method is the Bayesian approach. An important issue in the Bayesian analysis of SEMs is model selection. In the literature, Bayes factor and deviance information criterion (DIC) are commonly used statistics for Bayesian model selection. However, as commented in Chen et al. (2004), Bayes factor relies on posterior model probabilities, in which proper prior distributions are needed. And specifying prior distributions for all models under consideration is usually a challenging task, in particular when the model space is large. In addition, it is well known that Bayes factor and posterior model probability are generally sensitive to the choice of the prior distributions of the parameters. Furthermore the computational burden of Bayes factor is heavy. Alternatively, criterion-based methods are attractive in the sense that they do not require proper prior distributions in general, and the computation is quite simple. One of commonly used criterion-based methods is DIC, which however assumes the posterior mean to be a good estimator. For some models like the mixture SEMs, WinBUGS does not provide the DIC values. Moreover, if the difference in DIC values is small, only reporting the model with the smallest DIC value may be misleading. In this thesis, motivated by the above limitations of the Bayes factor and DIC, a Bayesian model selection criterion called the Lv measure is considered. It is a combination of the posterior predictive variance and bias, and can be viewed as a Bayesian goodness-of-fit statistic. The calibration distribution of the Lv measure, defined as the prior predictive distribution of the difference between the Lv measures of the candidate model and the criterion minimizing model, is discussed to help understanding the Lv measure in detail. The computation of the Lv measure is quite simple, and the performance is satisfactory. Thus, it is an attractive model selection statistic. In this thesis, the application of the Lv measure to various kinds of SEMs will be studied, and some illustrative examples will be conducted to evaluate the performance of the Lv measure for model selection of SEMs. To compare different model selection methods, Bayes factor and DIC will also be computed. Moreover, different prior inputs and sample sizes are considered to check the impact of the prior information and sample size on the performance of the Lv measure. In this thesis, when the performances of two models are similar, the simpler one is selected. / Li, Yunxian. / Adviser: Song Xinyuan. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 116-122). / 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.

by Fan Xuqian. / "August 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 84-87). / 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.