Bayesian latent variable models with complex data types

Ph.D.Given the diversity of real problems, complex data types such as partially ordered data, semi-continuous data and neuroimaging data are frequently encountered in psychology, sociology, and biomedical fields. However, besides the complexity of data type, the characteristic of the data, for example, time dependency, multicollinearity, high dimensionality and missingness should also be taken into consideration. In this thesis, three Bayesian models, including two-level model for repeated partially ordered data, two-part structural equation model for semi-continuous data, and latent factor-on-image regression model with missing data, are proposed. Apart from coefficient estimation, variable selection using spike-and-slab least absolute shrinkage and selection operator is also considered for selecting influential predictors. Markov chain Monte Carlo algorithm with Gibbs sampling method are derived for the Bayesian inference. Simulation studies demonstrate that performance of the proposed methods is satisfactory. The proposed methods are utilized to analyze real data sets in social psychological and biomedical sciences fields to gain insights into the real problems.現實問題多種多樣，故而複雜類型的數據層見迭出，例如部分有序數據、半連續數據、腦神經影像數據皆常見於心理學、社會學、生物醫學研究領域。此外，數據之特性例如時間相依性、多重共線性、不完整性亦需被妥善處理。本文提出三個貝葉斯模型，即基於部分有序數據的二層次模型、基於半連續數據的二部分模型、以及帶有缺失數據的潛變量-圖像回歸模型。除卻參數估計問題，本文還考慮了基於spike-and-slab lasso的變量選擇問題。在貝葉斯推斷中，我們使用了馬爾科夫連蒙特卡羅算法與吉布斯抽樣方法。本文中的方法，在仿真研究中的成效令人滿意。我們還將本文方法應用於社會心理學、生物醫學領域的實際數據分析，對相關實際問題給出更進一步的解釋。Wang, Xiaoqing.Thesis Ph.D. Chinese University of Hong Kong 2019.Includes bibliographical references (leaves 120-138).Abstracts also in Chinese.Title from PDF title page (viewed on 07, December, 2020)