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P. Ballesteros-Pérez, M.C. González-Cruz, D. Mora-Melià (2018) EXPLAINING THE BAYES’ THEOREM GRAPHICALLY, INTED2018 Proceedings, pp. 1608-1614.pdf (601.8 kB)

# Explaining the Bayes' theorem graphically

conference contribution
posted on 2018-11-26, 11:58 authored by Pablo Ballesteros-Perez, M. Carmen Gonzalez-Cruz, Daniel Mora-Melia
The Bayes’ theorem on conditional probabilities is normally presented to students in introductory courses/modules on Statistics and Probability. This because most STEM students will make use of conditional probabilities in their professional lives with or without noticing. However, maybe because of the unfamiliar notation or because of the variety of ways in which this theorem can be formulated, most students have trouble understanding it. Moreover, when it comes to practical applications and problem exercises, most students (who have generally memorised its manifold ways of rearranging the conditional probabilities formula along with a few applications) struggle even more to come up with correct solutions. By means of a completely graphical approach, this paper presents an alternative way of explaining the Bayes’ theorem to STEM students. By means of diagrams and schematics the students can see the conditional probabilities represented as areas in a square. Simple geometric operations with these areas (additions and multiplications mostly) allow them, not just to understand this theorem far quicker, but to apply it confidently in almost any possible problem configuration. Overall, this paper offers an alternative or complementary way of explaining this important theorem more clearly to students that take probability courses by conveying it graphically instead of with the traditional mathematical formulae. Through a representative case study, this paper deals provides first-hand evidence about how confusing to understand the Bayes’ theorem might be at first even in simple problems, and how the understanding of this theorem is dramatically improved when presenting it graphically.

## School

• Architecture, Building and Civil Engineering

## Published in

12TH INTERNATIONAL TECHNOLOGY, EDUCATION AND DEVELOPMENT CONFERENCE (INTED)

1608 - 1614

## Citation

BALLESTEROS-PEREZ, P., GONZALEZ-CRUZ, M.C. and MORA-MELIA, D., 2018. Explaining the Bayes' theorem graphically. IN: Gomez Chova, L., Lopez Martinez, A. and Candel Torres, I. (eds.) 12th International Technology, Education and Development Conference (INTED 2018 conference proceedings), Valencia, Spain, March 5-7th. Valencia: IATED Academy, pp. 1608-1614.

## Version

• VoR (Version of Record)

## Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

2018

## Notes

This is a conference paper. The publisher's preferred citation format is P. Ballesteros-Pérez, M.C. González-Cruz, D. Mora-Melià (2018) EXPLAINING THE BAYES’ THEOREM GRAPHICALLY, INTED2018 Proceedings, pp. 1608-1614.

9788469794807

2340-1079

• en

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