Social learning has been shown to be an evolutionarily adaptive strategy, but it can be implemented via many different cognitive mechanisms. The adaptive advantage of social learning depends crucially on the ability of each learner to obtain relevant and accurate information from informants. The source of informants' knowledge is a particularly…

Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-conditional independence of features. This feature independence assumption simplifies the inference…

Interest in Bayesian analysis of item response theory (IRT) models has grown tremendously due to the appeal of the paradigm among psychometricians, advantages of these methods when analyzing complex models, and availability of general-purpose software. Possible models include models which reflect multidimensionality due to designed test structure,…

The structure of natural languages give rise to many dependencies in the linear sequences of words, and within words themselves. Detecting these dependencies is arguably critical for young children in learning the underlying structure of their language. There is considerable evidence that human adults and infants are sensitive to the statistical…

Like scientists, children seek ways to explain causal systems in the world. But are children scientists in the strict Bayesian tradition of maximizing posterior probability? Or do they attend to other explanatory considerations, as laypeople and scientists--such as Einstein--do? Four experiments support the latter possibility. In particular, we…

In this paper, we investigate two purported problems with Bayesian Knowledge Tracing (BKT), a popular statistical model of student learning: "identifiability" and "semantic model degeneracy." In 2007, Beck and Chang stated that BKT is susceptible to an "identifiability problem"--various models with different…

In past decades, researchers have conducted a myriad of masked priming lexical decision experiments aimed at unveiling the early processes underlying lexical access. A relatively overlooked question is whether a masked unrelated wordlike/unwordlike prime influences the processing of the target stimuli. If participants apply to the primes the same…

With the development of technology-enhanced learning platforms, eye-tracking biometric indicators can be recorded simultaneously with students item responses. In the current study, visual fixation, an essential eye-tracking indicator, is modeled to reflect the degree of test engagement when a test taker solves a set of test questions. Three…

Multilevel data are a reality for many disciplines. Currently, although multiple options exist for the treatment of multilevel data, most disciplines strictly adhere to one method for multilevel data regardless of the specific research design circumstances. The purpose of this Monte Carlo simulation study is to compare several methods for the…

In "Maths for Business," a large first-year mathematics module, the continuous assessment component comprises 10 weekly quizzes which combine to contribute 40% of the final module mark. If students did not receive the full five marks on their weekly quiz, they were provided with the opportunity to resubmit their corrected weekly quiz…

This paper deals with a brief history of probability theory and its applications to Jacob Bernoulli's famous law of large numbers and theory of errors in observations or measurements. Included are the major contributions of Jacob Bernoulli and Laplace. It is written to pay the tricentennial tribute to Jacob Bernoulli, since the year 2013…

This paper reviews recent research on causal inference with large-scale assessments in education from a Bayesian perspective. I begin by adopting the potential outcomes model of Rubin ("J Educ Psychol" 66:688-701, 1974) as a framework for causal inference that I argue is appropriate with large-scale educational assessments. I then…

Models of category learning have been extensively studied in cognitive science and primarily tested on perceptual abstractions or artificial stimuli. In this paper, we focus on categories acquired from natural language stimuli, that is, words (e.g., "chair" is a member of the furniture category). We present a Bayesian model that, unlike…

This study models graduation rates at 4-year broad access institutions (BAIs). We examine the student body, structural-demographic, and financial characteristics that best predict 6-year graduation rates across two time periods (2008-2009 and 2014-2015). A Bayesian model averaging approach is utilized to account for uncertainty in variable…

Stan is a flexible probabilistic programming language providing full Bayesian inference through Hamiltonian Monte Carlo algorithms. The benefits of Hamiltonian Monte Carlo include improved efficiency and faster inference, when compared to other MCMC software implementations. Users can interface with Stan through a variety of computing…