Short Communication

Year 2021,
Volume: 18 Issue: 1, 61 - 71, 01.05.2021
### Abstract

### References

- [1] Nguyen, H. T., & Thach, N. N., “A Panorama of Applied Mathematical Problems in Economics”, Thai Journal of Mathematics, 2018.
- [2] Sahai, H., “Teaching Bayes' Theorem using examples in medical diagnosis”, Teaching Mathematics and its Applications: An International Journal of the IMA, vol. 11(4), pp. 175-179, 1992.
- [3] Kolb, B. G., “Brain plasticity and behavior”, Current Directions in Psychological Science, vol. 12(1), pp. 1-5, 2003.
- [4] Florens, J. P., “Elements of Bayesian Statistics”, New York: Taylor & Francis Inc, 2019.
- [5] Green, K. a., “Reorganizing freshman business mathematics, I: background and philosophy”, Teaching Mathematics and its Applications. An International Journal of the IMA, vol. 27(1), pp. 11-23, 2008.
- [6] Bolstad, W. M., “Teaching Bayesian statistics to undergraduates: Who, what, where, when, why, and how”, Proceedings of the Sixth International Conference on Teaching of Statistics, 2002.
- [7] Lecoutre, B., “Training students and researchers in Bayesian methods”, Journal of Data Science, vol. 4(2), pp. 207-232, 2006.
- [8] Holt, C. A., “Classroom games: Understanding bayes' rule”, Journal of Economic Perspectives, vol. 10(2), pp. 179-187, 1996.
- [9] Sedlmeier, P. &., “Teaching Bayesian reasoning in less than two hours”, Journal of experimental psychology: general, vol. 130(3), pp. 380, 2001.
- [10] Kurzenhäuser, S. &., “Teaching Bayesian reasoning: an evaluation of a classroom tutorial for medical students”, Medical Teacher, vol. 24(5), pp. 516-521, 2002.
- [11] Gelman, A. C., “Bayesian data analysis (2nd ed.)”, London: Chapman and Hall, 2004.
- [12] Jackman, S., “Bayesian analysis for the social sciences”, Chichester, United Kingdom: John Wiley & Sons, 2009.
- [13] Kruschke, J. K., “Bayesian estimation supersedes the t test”, Journal of Experimental Psychology: General, vol. 142(2), pp. 573, 2013.
- [14] Faulkenberry, T. J., “A Simple Method for Teaching Bayesian Hypothesis Testing in the Brain and Behavioral Sciences”, Journal of Undergraduate Neuroscience Education, vol. 16(2), pp. 126-130, 2018.
- [15] Rouder, J. N., “Teaching Bayes’ theorem: Strength of evidence as predictive accuracy”, The American Statistician, vol. 73(2), pp. 186-190, 2019.
- [16] Rässler, S., “Statistical matching: A frequentist theory, practical applications, and alternative Bayesian approaches”, Springer Science & Business Media, vol. 168, 2012.
- [17] Walpole, R. E., “Essentials of Probability and Statistics”, Pearson, 2013.
- [18] Pishro-Nik, H., “Introduction to probability, statistics, and random processes”, Kappa Research LLC, 2014.
- [19] Anderson, D. R., “Statistics for business & economics”, Cengage, 2015.
- [20] Leon-Garcia, A., “Probability, statistics, and random processes for electrical engineering”, Pearson, 2017.
- [21] Render, B. S., “Quantitative analysis for management (13 ed.)”, Pearson, 2018.
- [22] Giri, N. C., “Introduction to Probability and Statistics”, Taylor and Francis, 2019.
- [23] Walpole, R. E., “Introduction to Statistics”, New York: Macmillan, 1982.

Year 2021,
Volume: 18 Issue: 1, 61 - 71, 01.05.2021
### Abstract

### References

Probability and Statistics are difficult courses to learn by the statistics students and thus

giving a challenging job for the instructors to teach. Among the many topics, most

commonly, Bayes’ theorem and its associated probabilities is one common area which

causes a lot of stir in teaching and learning. In such difficult scenarios, the instructor’s

teaching pedagogy plays a vital role to inculcate correct knowledge to the students, as

required. In this paper we have discussed probability tree diagrams and presented that

they are better off to help understand and teach Bayes’ theorem with a completeness of

process thinking. Tree diagrams methodology is presented on varying examples –simple

to difficult as a prove of its generalization and entireness in statistics learning of Bayes’

probabilities. This is an instructional article, in which an innovative pedagogy for

teaching Bayes’ theorem is discussed. We have provided a scholarly argument to justify

for considering its wider use. There is no claim that the proposed method is simpler from

presently used methods but however this is claimed that this will unleash the details of

Bayes’ probabilities which are neither taught in the class nor emphasized in the texts.

- [1] Nguyen, H. T., & Thach, N. N., “A Panorama of Applied Mathematical Problems in Economics”, Thai Journal of Mathematics, 2018.
- [2] Sahai, H., “Teaching Bayes' Theorem using examples in medical diagnosis”, Teaching Mathematics and its Applications: An International Journal of the IMA, vol. 11(4), pp. 175-179, 1992.
- [3] Kolb, B. G., “Brain plasticity and behavior”, Current Directions in Psychological Science, vol. 12(1), pp. 1-5, 2003.
- [4] Florens, J. P., “Elements of Bayesian Statistics”, New York: Taylor & Francis Inc, 2019.
- [5] Green, K. a., “Reorganizing freshman business mathematics, I: background and philosophy”, Teaching Mathematics and its Applications. An International Journal of the IMA, vol. 27(1), pp. 11-23, 2008.
- [6] Bolstad, W. M., “Teaching Bayesian statistics to undergraduates: Who, what, where, when, why, and how”, Proceedings of the Sixth International Conference on Teaching of Statistics, 2002.
- [7] Lecoutre, B., “Training students and researchers in Bayesian methods”, Journal of Data Science, vol. 4(2), pp. 207-232, 2006.
- [8] Holt, C. A., “Classroom games: Understanding bayes' rule”, Journal of Economic Perspectives, vol. 10(2), pp. 179-187, 1996.
- [9] Sedlmeier, P. &., “Teaching Bayesian reasoning in less than two hours”, Journal of experimental psychology: general, vol. 130(3), pp. 380, 2001.
- [10] Kurzenhäuser, S. &., “Teaching Bayesian reasoning: an evaluation of a classroom tutorial for medical students”, Medical Teacher, vol. 24(5), pp. 516-521, 2002.
- [11] Gelman, A. C., “Bayesian data analysis (2nd ed.)”, London: Chapman and Hall, 2004.
- [12] Jackman, S., “Bayesian analysis for the social sciences”, Chichester, United Kingdom: John Wiley & Sons, 2009.
- [13] Kruschke, J. K., “Bayesian estimation supersedes the t test”, Journal of Experimental Psychology: General, vol. 142(2), pp. 573, 2013.
- [14] Faulkenberry, T. J., “A Simple Method for Teaching Bayesian Hypothesis Testing in the Brain and Behavioral Sciences”, Journal of Undergraduate Neuroscience Education, vol. 16(2), pp. 126-130, 2018.
- [15] Rouder, J. N., “Teaching Bayes’ theorem: Strength of evidence as predictive accuracy”, The American Statistician, vol. 73(2), pp. 186-190, 2019.
- [16] Rässler, S., “Statistical matching: A frequentist theory, practical applications, and alternative Bayesian approaches”, Springer Science & Business Media, vol. 168, 2012.
- [17] Walpole, R. E., “Essentials of Probability and Statistics”, Pearson, 2013.
- [18] Pishro-Nik, H., “Introduction to probability, statistics, and random processes”, Kappa Research LLC, 2014.
- [19] Anderson, D. R., “Statistics for business & economics”, Cengage, 2015.
- [20] Leon-Garcia, A., “Probability, statistics, and random processes for electrical engineering”, Pearson, 2017.
- [21] Render, B. S., “Quantitative analysis for management (13 ed.)”, Pearson, 2018.
- [22] Giri, N. C., “Introduction to Probability and Statistics”, Taylor and Francis, 2019.
- [23] Walpole, R. E., “Introduction to Statistics”, New York: Macmillan, 1982.

There are 23 citations in total.

Primary Language | English |
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Subjects | Engineering |

Journal Section | Articles |

Authors | |

Publication Date | May 1, 2021 |

Published in Issue | Year 2021 Volume: 18 Issue: 1 |