There is a wealth of evidence that people's reasoning is influenced by explanatory considerations. Little is known, however, about the exact form this influence takes, for instance about whether the influence is unsystematic or because of people's following some rule. Three experiments investigate the descriptive adequacy of a precise proposal to…

Recall of remembered locations reliably reflects a compromise between a target's true position and its region's prototypical position. The effect is quite robust, and a standard interpretation for these data is that the metric and categorical codings blend in a Bayesian combinatory fashion. However, there has been no direct experimental evidence…

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…

In the coming years, public programs will capture even more and richer data than they do now, including data from web-based tools used by participants in employment services, from tablet-based educational curricula, and from electronic health records for Medicaid beneficiaries. Program evaluators seeking to take full advantage of these data…

Research on human causal induction has shown that people have general prior assumptions about causal strength and about how causes interact with the background. We propose that these prior assumptions about the parameters of causal systems do not only manifest themselves in estimations of causal strength or the selection of causes but also when…

P values have been critiqued on several grounds but remain entrenched as the dominant inferential method in the empirical sciences. In this article, we elaborate on the fact that in many statistical models, the one-sided "P" value has a direct Bayesian interpretation as the approximate posterior mass for values lower than zero. The…

Teaching some concepts in statistics greatly benefits from individual practice with immediate feedback. In order to provide such practice to a large number of students we have written a simulator based on an historical event: the loss in May 22, 1968, and subsequent search for the nuclear submarine USS Scorpion. Students work on a simplified…

Modeling student learning processes is highly complex since it is influenced by many factors such as motivation and learning habits. The high volume of features and tools provided by computer-based learning environments confounds the task of tracking student knowledge even further. Deep Learning models such as Long-Short Term Memory (LSTMs) and…

While interest in Bayesian statistics has been growing in statistics education, the treatment of the topic is still inadequate in both textbooks and the classroom. Because so many fields of study lead to careers that involve a decision-making process requiring an understanding of Bayesian methods, it is becoming increasingly clear that Bayesian…

Four experiments examined the locus of impact of causal knowledge on consideration of alternative hypotheses in judgments under uncertainty. Two possible loci were examined; overcoming neglect of the alternative when developing a representation of a judgment problem and improving utilization of statistics associated with the alternative…

We tested a method for solving Bayesian reasoning problems in terms of spatial relations as opposed to mathematical equations. Participants completed Bayesian problems in which they were given a prior probability and two conditional probabilities and were asked to report the posterior odds. After a pretraining phase in which participants completed…

Current developments in the statistics community suggest that modern statistics education should be structured holistically, that is, by allowing students to work with real data and to answer concrete statistical questions, but also by educating them about alternative frameworks, such as Bayesian inference. In this article, we describe how we…

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…

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…