Foundations of statistics research aims to establish fundamental principles guiding inference about populations under uncertainty. It is concerned with the process of learning from observations, notions of uncertainty and induction, and satisfying inferential objectives. The growing interest in predictive methods in high-stakes fields like…

Categorical data become increasingly ubiquitous in the modern big data era. In this dissertation, we propose novel statistical learning and inference methods for large-scale categorical data, focusing on latent variable models and their applications to psychometrics. In psychometric assessments, the subjects' underlying aptitude often cannot be…

The development in information science has enabled an explosive growth of data, which attracts more and more researchers to engage in the field of big data analytics. Noticeably, in many real-world applications, large amounts of data are imbalanced data since the events of interests occur infrequently. Classification of imbalanced data is an…

There are two primary challenges for instructors in offering a high-quality course at large scale. The first is scaling educational experiences to such a large audience. The second major challenge encountered is that of enabling adaptivity of the educational experience. This thesis addresses both major challenges in the way of high-quality…

Many methods exist for imputing missing data but fewer methods have been proposed to test the missing data mechanism. Little (1988) introduced a multivariate chi-square test for the missing completely at random data mechanism (MCAR) that compares observed means for each pattern with expectation-maximization (EM) estimated means. As an alternative,…