One of the fundamental tasks in science is to find explainable relationships between observed phenomena. Recent work has addressed this problem by attempting to learn the structure of graphical models - especially Gaussian models - by the imposition of sparsity constraints. The graphical lasso is a popular method for learning the structure of a Gaussian model. It uses regularisation to impose sparsity. In real-world problems, there may be latent variables that confound the relationships between the observed variables. Ignoring these latents, and imposing sparsity in the space of the visibles, may lead to the pruning of important structural relationships. We address this problem by introducing an expectation maximisation (EM) method for learning a Gaussian model that is sparse in the joint space of visible and latent variables. By extending this to a conditional mixture, we introduce multiple structures, and allow side information to be used to predict which structure is most appropriate for each data point. Finally, we handle non-Gaussian data by extending each sparse latent Gaussian to a Gaussian copula. We train these models on a financial data set; we find the structures to be interpretable, and the new models to perform better than their existing competitors. A potential problem with the mixture model is that it does not require the structure to persist in time, whereas this may be expected in practice. So we construct an input-output HMM with sparse Gaussian emissions. But the main result is that, provided the side information is rich enough, the temporal component of the model provides little benefit, and reduces efficiency considerably. The GWishart distribution may be used as the basis for a Bayesian approach to learning a sparse Gaussian. However, sampling from this distribution often limits the efficiency of inference in these models. We make a small change to the state-of-the-art block Gibbs sampler to improve its efficiency. We then introduce a Hamiltonian Monte Carlo sampler that is much more efficient than block Gibbs, especially in high dimensions. We use these samplers to compare a Bayesian approach to learning a sparse Gaussian with the (non-Bayesian) graphical lasso. We find that, even when limited to the same time budget, the Bayesian method can perform better. In summary, this thesis introduces practically useful advances in structure learning for Gaussian graphical models and their extensions. The contributions include the addition of latent variables, a non-Gaussian extension, (temporal) conditional mixtures, and methods for efficient inference in a Bayesian formulation.

Chen, Qiuting. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 71-74). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview --- p.1 / Chapter 1.2 --- Bayesian Approach --- p.3 / Chapter 1.3 --- Outline of the thesis --- p.5 / Chapter 2 --- Model Descriptions --- p.6 / Chapter 2.1 --- Basic Latent Curve Models --- p.6 / Chapter 2.2 --- Latent Curve Models with Exogenous Latent Variables --- p.8 / Chapter 2.3 --- Latent Curve Models with both Exogenous Variables and Longitudinal La- tent Variables --- p.9 / Chapter 2.4 --- multisample analysis --- p.12 / Chapter 3 --- Bayesian Estimation and Model Comparison --- p.18 / Chapter 3.1 --- Bayesian analysis for parameter estimation --- p.18 / Chapter 3.2 --- Bayesian model comparison --- p.27 / Chapter 4 --- A simulation study --- p.31 / Chapter 4.1 --- Simulation for parameter estimations --- p.31 / Chapter 4.2 --- Simulation for model comparison using DIC --- p.35 / Chapter 5 --- An illustrative example --- p.47 / Chapter 5.1 --- Background introduction --- p.47 / Chapter 5.2 --- Some firm-specific factors that may affect the capital structure --- p.49 / Chapter 5.3 --- Real data illustration --- p.52 / Chapter 6 --- Conclusion and further discussion --- p.65 / Appendix --- p.67 / Chapter 7 --- Appendix: equation derivation --- p.67 / Bibliography

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Travel Demand Management (TDM) is now considered one of the most important aspects of transportation planning and operation. The prime objective of TDM is to develop a sustainable transportation system utilizing the existing infrastructure. It is now a well known fact that excessive use of single occupancy vehicle causes numerous problems like traffic congestion, environmental pollution etc. Thus, from TDM perspective, it is of great importance to analyze travel behaviour in order to influence people to reduce car use and choose more sustainable modes such as carpool, public transit, park & ride, walk, bike etc. This study attempts an in-depth analysis of commuting mode choice behaviour using workplace commuter survey data from the City of Edmonton. Unlike traditional mode choice models, this study uses both instrumental and latent variables to better understand the choice process and analyzes their sensitivities with respect to TDM policies. / Transportation Engineering

Thesis (Ph.D.)--McMaster University, 2004. / Supervisors: John F. MacGregor, Theodora Kourti. Includes bibliographical references (leaves 221-227). Also available via World Wide Web.

Thesis (Ph.D.) -- McMaster University, 1998. / Includes bibliographical references (leaves 169-173). Also available via World Wide Web.

abstract: Statistical mediation analysis has been widely used in the social sciences in order to examine the indirect effects of an independent variable on a dependent variable. The statistical properties of the single mediator model with manifest and latent variables have been studied using simulation studies. However, the single mediator model with latent variables in the Bayesian framework with various accurate and inaccurate priors for structural and measurement model parameters has yet to be evaluated in a statistical simulation. This dissertation outlines the steps in the estimation of a single mediator model with latent variables as a Bayesian structural equation model (SEM). A Monte Carlo study is carried out in order to examine the statistical properties of point and interval summaries for the mediated effect in the Bayesian latent variable single mediator model with prior distributions with varying degrees of accuracy and informativeness. Bayesian methods with diffuse priors have equally good statistical properties as Maximum Likelihood (ML) and the distribution of the product. With accurate informative priors Bayesian methods can increase power up to 25% and decrease interval width up to 24%. With inaccurate informative priors the point summaries of the mediated effect are more biased than ML estimates, and the bias is higher if the inaccuracy occurs in priors for structural parameters than in priors for measurement model parameters. Findings from the Monte Carlo study are generalizable to Bayesian analyses with priors of the same distributional forms that have comparable amounts of (in)accuracy and informativeness to priors evaluated in the Monte Carlo study. / Dissertation/Thesis / Doctoral Dissertation Psychology 2017

In this thesis, we focus on the the comparison of treatments with ordered categorical responses. The three cases of treatment comparisons will all be studied. The main objective of this thesis is to develop more effective comparison methods for treatments with ordinal responses and to address some important issues involved in different comparison problems. Our major statistical approach is to consider ordinal responses as manifestations of some underlying continuous random variables. / The comparison of treatments to detect possible treatment effects is a very important topic in statistical research. It has been drawing significant interests from both academicians and practitioners. Important research work on treatment comparisons dates back several decades. For treatment comparisons, the following three cases are very common: the comparison of two independent treatments; the comparison of treatments with repeated measurements; and the multiple comparison of several treatments. For different cases, the involved research issues are usually different. In many fields of study, the level of measurement for responses of the treatments is ordinal. Many examples can be found in areas such as biostatistics, psychology, sociology, and market research, where the ordered categorical variables play an important role. / This thesis consists of three main parts. In the first part, we consider the modeling of treatments with longitudinal ordinal responses by a latent growth curve. On the basis of such a latent growth curve, we achieve a comprehensive flexible model with straightforward interpretations and a variety of applications including treatment comparison, the analysis of covariates, and equivalence test of treatments. In the second part, we consider the comparison of several treatments with a control for ordinal responses. By considering the ordinal responses as manifestations of some underlying normal random variables, a latent normal distribution model is utilized and the corresponding parameter estimation method is proposed. Further, we also derive testing procedures that compare several treatments with a control under an analytical framework. Both single-step and stepwise procedures are introduced, and these procedures are compared in terms of average power based on a simulation study. In the last part of this thesis, we establish a unified framework for treatment comparisons with ordinal responses, which allows various treatment comparison methods be comprehended using a unified perspective. The latent variable model is also utilized, but the underlying random variables are allowed to have any member of the location-scale distribution family. This latent variable model under such a specification of underlying distributions subsumes many existing models in the literature. A two-step procedure to identify the model and produce the parameter estimates is proposed. Based on this procedure, many important statistical inferences can be conveniently conducted. Furthermore, the sample size determination method based on the latent variable method is also proposed. The proposed latent variable method is compared with the existing methods in terms of power and sample size. / Lu, Tongyu. / Adviser: Wai-Yin Poon. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 94-101). / 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.

Wing-Yeong Lee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 73-75). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- The observed data --- p.3 / Chapter 1.3 --- Outline of the thesis --- p.8 / Chapter Chapter 2 --- Modeling using Latent Variable --- p.9 / Chapter Chapter 3 --- Imputation Procedure --- p.16 / Chapter 3.1 --- Introduction --- p.16 / Chapter 3.2 --- Introduction to Metropolis-Hastings algorithm --- p.18 / Chapter 3.3 --- Introduction to Gibbs sampler --- p.19 / Chapter 3.4 --- Imputation step --- p.21 / Chapter 3.5 --- Initialization of the missing values by regression --- p.23 / Chapter 3.6 --- Initialization of the parameters and creating the latent variable and noises --- p.27 / Chapter 3.7 --- Simulation of Y's --- p.30 / Chapter 3.8 --- Simulation of the parameters --- p.34 / Chapter 3.9 --- Simulation of T by use of the Metropolis-Hastings algorithm --- p.41 / Chapter 3.10 --- Distribution of Vij's given all other values --- p.44 / Chapter 3.11 --- Simulation procedure of Vij's --- p.46 / Chapter Chapter 4 --- Data Analysis of the Pollutant Data --- p.48 / Chapter 4.1 --- Convergence of the process --- p.48 / Chapter 4.2 --- Data analysis --- p.53 / Chapter Chapter 5 --- Conclusion --- p.69 / REFERENCES --- p.73

Video games are played by more than 1.8 billion people and are a pervasive force in society, but despite decades of research there has been little consensus on their effects. Before we are able to model complex outcomes such as excessive engagement, we must first understand how and why people play video games. This dissertation integrates latent factor models with techniques from machine learning and network analysis to develop a holistic picture of gaming style, motivations, and individual differences. It employs diverse sources of data across several studies and a total of 2,143 participants, combining online questionnaires with qualitative analysis of participant responses and objective information about gaming behaviour from the API of the popular gaming network "Steam", and finds that stress relief is a primary motivation for engaging in the immersive worlds of video games. Previous research has indicated three underlying factors of Immersion, Achievement and Socialising which replicated across three comprehensive studies of 480 adults, 106 adults and children with an Autism Spectrum Condition, and 961 adults and adolescents. Gamers experiencing more stress in their daily lives were more likely to have Immersion rather than Social or Achievement play styles. Achievement-oriented gamers tended to be lower in stress, higher in conscientiousness and emotional stability, and played more than Immersion-focused gamers. A qualitative analysis of 54 gamers' descriptions of why they recently chose to play a game was used to develop the "Reasons for Playing Video Games" items (RPVG), which were administered to independent samples of 243, 299 and 961 gamers. The qgraph R package was used to perform network analyses of the RPVG items and gameplay style factors, employing the machine learning-based adaptive LASSO technique to estimate a partial correlation matrix from a set of variables as a Pairwise Markov Random Field. Gamers higher in Immersion tended to play for escapism, distraction, and fantasy, while social gamers played for excitement, energy, and self-expression. Network analysis and graph theory illustrate the central role of stress relief in the network of Reasons for Playing Video Games and shows that playing when feeling stressed is strongly linked with Immersion.