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Article

How to Train Novices in Bayesian Reasoning

1
Institute of Mathematics, University of Kassel, 34132 Kassel, Germany
2
Faculty of Mathematics, University of Regensburg, 93053 Regensburg, Germany
3
Institute of Mathematics, Ludwig-Maximilians-University Munich, 80333 München, Germany
4
Department of Mathematics Education, University of Freiburg, 79104 Freiburg, Germany
5
Institute of Mathematics, University of Education Heidelberg, 69120 Heidelberg, Germany
*
Author to whom correspondence should be addressed.
Mathematics 2022, 10(9), 1558; https://doi.org/10.3390/math10091558
Submission received: 15 March 2022 / Revised: 22 April 2022 / Accepted: 28 April 2022 / Published: 5 May 2022
(This article belongs to the Special Issue Statistics Education: An Immediate Need in a Changing World)

Abstract

Bayesian Reasoning is both a fundamental idea of probability and a key model in applied sciences for evaluating situations of uncertainty. Bayesian Reasoning may be defined as the dealing with, and understanding of, Bayesian situations. This includes various aspects such as calculating a conditional probability (performance), assessing the effects of changes to the parameters of a formula on the result (covariation) and adequately interpreting and explaining the results of a formula (communication). Bayesian Reasoning is crucial in several non-mathematical disciplines such as medicine and law. However, even experts from these domains struggle to reason in a Bayesian manner. Therefore, it is desirable to develop a training course for this specific audience regarding the different aspects of Bayesian Reasoning. In this paper, we present an evidence-based development of such training courses by considering relevant prior research on successful strategies for Bayesian Reasoning (e.g., natural frequencies and adequate visualizations) and on the 4C/ID model as a promising instructional approach. The results of a formative evaluation are described, which show that students from the target audience (i.e., medicine or law) increased their Bayesian Reasoning skills and found taking part in the training courses to be relevant and fruitful for their professional expertise.
Keywords: Bayesian Reasoning; Bayes’ rule; visualization; unit square; double tree; natural frequencies; 4C/ID model Bayesian Reasoning; Bayes’ rule; visualization; unit square; double tree; natural frequencies; 4C/ID model

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MDPI and ACS Style

Büchter, T.; Eichler, A.; Steib, N.; Binder, K.; Böcherer-Linder, K.; Krauss, S.; Vogel, M. How to Train Novices in Bayesian Reasoning. Mathematics 2022, 10, 1558. https://doi.org/10.3390/math10091558

AMA Style

Büchter T, Eichler A, Steib N, Binder K, Böcherer-Linder K, Krauss S, Vogel M. How to Train Novices in Bayesian Reasoning. Mathematics. 2022; 10(9):1558. https://doi.org/10.3390/math10091558

Chicago/Turabian Style

Büchter, Theresa, Andreas Eichler, Nicole Steib, Karin Binder, Katharina Böcherer-Linder, Stefan Krauss, and Markus Vogel. 2022. "How to Train Novices in Bayesian Reasoning" Mathematics 10, no. 9: 1558. https://doi.org/10.3390/math10091558

APA Style

Büchter, T., Eichler, A., Steib, N., Binder, K., Böcherer-Linder, K., Krauss, S., & Vogel, M. (2022). How to Train Novices in Bayesian Reasoning. Mathematics, 10(9), 1558. https://doi.org/10.3390/math10091558

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