Simulation studies involving mixture models inevitably aggregate parameter estimates and other output across numerous replications. A primary issue that arises in these methodological investigations is label switching. The current study compares several label switching corrections that are commonly used when dealing with mixture models. A growth…

Digital educational technologies offer the potential to customize students' experiences and learn what works for which students, enhancing the technology as more students interact with it. We consider whether and when attempting to discover how to personalize has a cost, such as if the adaptation to personal information can delay the adoption of…

Searching for information is critical in many situations. In medicine, for instance, careful choice of a diagnostic test can help narrow down the range of plausible diseases that the patient might have. In a probabilistic framework, test selection is often modeled by assuming that people's goal is to reduce uncertainty about possible states of the…

Intelligent tutoring systems adapt the curriculum to the needs of the individual student. Therefore, an accurate representation and prediction of student knowledge is essential. Bayesian Knowledge Tracing (BKT) is a popular approach for student modeling. The structure of BKT models, however, makes it impossible to represent the hierarchy and…

The thesis explores efficient learning algorithms in settings which are more restrictive than the PAC model of learning (Valiant) in one of the following two senses: (i) The learning algorithm has a very weak access to the unknown function, as in, it does not get labeled samples for the unknown function (ii) The error guarantee required from the…

Personalization, the idea that teaching can be tailored to each students' needs, has been a goal for the educational enterprise for at least 2,500 years (Regian, Shute, & Shute, 2013, p.2). Recently personalization has picked up speed with the advent of mobile computing, the Internet and increases in computer processing power. These changes…

A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…

As adaptive tutoring systems grow increasingly popular for the completion of classwork and homework, it is crucial to assess the manner in which students are scored within these platforms. The majority of systems, including ASSISTments, return the binary correctness of a student's first attempt at solving each problem. Yet for many teachers,…

A long-standing challenge for knowledge tracing is how to update estimates of multiple subskills that underlie a single observable step. We characterize approaches to this problem by how they model knowledge tracing, fit its parameters, predict performance, and update subskill estimates. Previous methods allocated blame or credit among subskills…

In Probability and Statistics taught to mathematicians as a first introduction or to a non-mathematical audience, joint independence of events is introduced by requiring that the multiplication rule is satisfied. The following statement is usually tacitly assumed to hold (and, at best, intuitively motivated): If the n events E[subscript 1],…

The paper proposes a composite likelihood estimation approach that uses bivariate instead of multivariate marginal probabilities for ordinal longitudinal responses using a latent variable model. The model considers time-dependent latent variables and item-specific random effects to be accountable for the interdependencies of the multivariate…

A hypothetical framework to characterize statistical knowledge for teaching (SKT) is described. Empirical grounding for the framework is provided by artifacts from an undergraduate course for prospective teachers that concentrated on the development of SKT. The theoretical notion of "key developmental understanding" (KDU) is used to identify…

This dissertation is a compilation of several studies that are united by their relevance to probabilistic judgment aggregation. In the face of complex and uncertain events, panels of judges are frequently consulted to provide probabilistic forecasts, and aggregation of such estimates in groups often yield better results than could have been made…

Steinley and Brusco (2011) presented the results of a huge simulation study aimed at evaluating cluster recovery of mixture model clustering (MMC) both for the situation where the number of clusters is known and is unknown. They derived rather strong conclusions on the basis of this study, especially with regard to the good performance of…

Under the normative Expected Value (EV) model, multiple outcomes are additive, but in everyday worth judgement intuitive averaging prevails. Young children also use averaging in EV judgements, leading to a disordinal, crossover violation of utility when children average the part worths of simple gambles involving independent events (Schlottmann,…