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…

In this paper different type of mathematical explanations are presented in relation to the mathematical problem of probabilities Monty Hall (card version) and the computational tool Latent Semantic Analyses (LSA) is used. At the moment the results in the literature about this computational tool to study texts show that this technique is…

For any density function (or probability function), there always corresponds a "cumulative distribution function" (cdf). It is a well-known mathematical fact that the cdf is more general than the density function, in the sense that for a given distribution the former may exist without the existence of the latter. Nevertheless, while the…

A central puzzle for theories of choice is that people's preferences between options can be reversed by the presence of decoy options (that are not chosen) or by the presence of other irrelevant options added to the choice set. Three types of reversal effect reported in the decision-making literature, the attraction, compromise, and similarity…

This extension of Harris' classification system permits classification of the interval-scale properties of any 2 x 2 (two person, two choice) game. The system is compared to taxonomies developed by various previous researchers. It is shown to permit compact description of any 2 x 2 game as an octet of numbers. It also permits rapid classification…

Some counterintuitive ideas in probability are examined. In particular, for sequential selection procedure, such as drawing cards, it is shown that there is probabilistic advantage to drawing first (or early) relative to drawing last (or late) in the sequence. (Author/MK)

DECIDE is a teacher-friendly, integrated approach designed to stimulate learning by allowing students to make decisions about situations they face in their lives while using scientific weather principles. This learning unit integrates weather science, decision theory, mathematics, statistics, geography, and reading in a context of decision…

The IADIS CELDA 2012 Conference intention was to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There had been advances in both cognitive psychology and computing that have affected the educational arena. The convergence of these two disciplines is increasing at a…