Place-based initiatives often use resident surveys to inform and evaluate interventions. Sampling based on well-defined sampling frames is important but challenging for initiatives that target subpopulations. Databases that enumerate total population counts can produce overinclusive sampling frames, resulting in costly outreach to ineligible…

Probabilistic machine learning increasingly informs critical decisions in medicine, economics, politics, and beyond. To aid the development of trust in these decisions, we develop a taxonomy delineating where trust in an analysis can break down: (1) in the translation of real-world goals to goals on a particular set of training data, (2) in the…

A fundamental aspect of statistical inference is representation of real-world data using statistical models. This article analyzes students' articulations of statistical models and modeling during their first steps in making informal statistical inferences. An integrated modeling approach (IMA) was designed and implemented to help students…

When performing a meta-analysis unexplained variation above that predicted by within study variation is usually modeled by a random effect. However, in some cases, this is not sufficient to explain all the variation because of outlier or unusual studies. A previously described method is to define an outlier as a study requiring a higher random…

Sampling tasks and sampling distributions provide a fertile realm for investigating students' conceptions of variability. A project-designed teaching episode on samples and sampling distributions was team-taught in 6 research classrooms (2 middle school and 4 high school) by the investigators and regular classroom mathematics teachers. Data…

A procedure modelling ideal classical and quantum gases is discussed. The proposed approach is mainly based on the idea that modelling and algorithm analysis can provide a deeper understanding of particularly complex physical systems. Appropriate representations and physical models able to mimic possible pseudo-mechanisms of functioning and having…

In 4 studies, the authors examined the hypothesis that the structure of the informational environment makes small samples more informative than large ones for drawing inferences about population correlations. The specific purpose of the studies was to test predictions arising from the signal detection simulations of R. B. Anderson, M. E. Doherty,…

When a simple random sample of size n is employed to establish a classification rule for prediction of a polytomous variable by an independent variable, the best achievable rate of misclassification is higher than the corresponding best achievable rate if the conditional probability distribution is known for the predicted variable given the…

Criteria for prediction of multinomial responses are examined in terms of estimation bias. Logarithmic penalty and least squares are quite similar in behavior but quite different from maximum probability. The differences ultimately reflect deficiencies in the behavior of the criterion of maximum probability.

The article by W. K. Estes marks a turning point in the mathematical learning theory movement. The central constructs were stimulus variability, stimulus sampling, and stimulus response association by contiguity, in a framework enabling prediction of response probability and latency. (SLD)

Until recently, norms of experimental reasoning have lacked systematic theoretical development. Thus, it has been easy for psychologists like Tversky and Kahneman to misclassify certain human reasoning processes as being Pascalian and invalid, rather than as being Baconian and valid. (CP)

This textbook for teaching reasoning processes and decision making under conditions of uncertainty is written at an introductory level. Based on a translation of a Hebrew book, the text is intended for the general training of military and civilian personnel required to process, sort, and/or evaluate incomplete, unreliable information. Potential…