During modern general election cycles, information to forecast the electoral outcome is plentiful. So-called fundamentals like economic growth provide information early in the cycle. Trial-heat polls become informative closer to Election Day. Our model builds on (Linzer, 2013) and is implemented in Stan (Team, 2020). We improve on the estimation…

Currently available (classical) testing procedures for the network autocorrelation can only be used for falsifying a precise null hypothesis of no network effect. Classical methods can be neither used for quantifying evidence for the null nor for testing multiple hypotheses simultaneously. This article presents flexible Bayes factor testing…

Bayesian analysts use informed priors to improve analytic precision and prediction; however, rarely have they applied a mixed methods approach that uses qualitative data to develop these priors. Yet, using qualitatively informed priors can be useful when making predictions in the context of small sample sizes, which is common in school-based…

We propose a semester-long Bayesian statistics course for undergraduate students with calculus and probability background. We cultivate students' Bayesian thinking with Bayesian methods applied to real data problems. We leverage modern Bayesian computing techniques not only for implementing Bayesian methods, but also to deepen students'…

We present an active-learning strategy for undergraduates that applies Bayesian analysis to candy-covered chocolate m&m's®. The exercise is best suited for small class sizes and tutorial settings, after students have been introduced to the concepts of Bayesian statistics. The exercise takes advantage of the nonuniform distribution of…

In behavioral sciences broadly, estimating growth models with Bayesian methods is becoming increasingly common, especially to combat small samples common with longitudinal data. Although Mplus is becoming an increasingly common program for applied research employing Bayesian methods, the limited selection of prior distributions for the elements of…

Skill prerequisite information is useful for tutoring systems that assess student knowledge or that provide remediation. These systems often encode prerequisites as graphs designed by subject matter experts in a costly and time-consuming process. In this paper, we introduce "Combined student Modeling and prerequisite Discovery"…

This teaching note gives a real-life example of Bayesian thinking. It discusses how credible accusations are that the outcome of the draw for the quarter-finals in the 2013 European Champions League Football was manipulated.

The appendices accompany the full report "Using Bayesian Meta-Analysis to Explore the Components of Early Literacy Interventions. WWC 2023-008," (ED630495), which pilots a new taxonomy developed by early literacy experts and intervention developers as part of a larger effort to develop standard nomenclature for the components of literacy…

BKT and other classical student models are designed for binary environments where actions are either correct or incorrect. These models face limitations in open-ended and data-driven environments where actions may be correct but non-ideal or where there may even be degrees of error. In this paper we present BKT-SR and RKT-SR: extensions of the…

This Snapshot highlights key findings from a study that used Bayesian stabilization to improve the reliability (long-term stability) of subgroup proficiency measures that the Pennsylvania Department of Education (PDE) uses to identify schools for Targeted Support and Improvement (TSI) or Additional Targeted Support and Improvement (ATSI). The…

To begin statistical analysis, Bayesians quantify their confidence in modeling hypotheses with priors. A prior describes the probability of a certain modeling hypothesis apart from the data. Bayesians should be able to defend their choice of prior to a skeptical audience. Collaboration between evaluators and stakeholders could make their choices…

Drawing valid inferences from modern measurement models is contingent upon a good fit of the data to the model. Violations of model-data fit have numerous consequences, limiting the usefulness and applicability of the model. As Bayesian estimation is becoming more common, understanding the Bayesian approaches for evaluating model-data fit models…

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the…

Abilities in scientific thinking and reasoning have been emphasized as core areas of initiatives, such as the Next Generation Science Standards or the College Board Standards for College Success in Science, which focus on the skills the future will demand of today's students. Although there is rich literature on studies of how these abilities…