Application of Monte-Carlo Simulation Towards a Better Understanding of Bayes’ Theorem in Engineering Education

Abstract

Bayes' Theorem (BT) is treated in probability theory and statistics. The BT shows how to change the probabilities a priori in view of new evidence, to obtain probabilities a posteriori. With the Bayesian interpretation of probability, the BT is expressed as the probability of an event (or the degree of belief in the occurrence of an event) should be changed, after considering evidence about the occurrence of that event. Bayesian inference is fundamental to Bayesian statistics. An example of practical application of this theorem in Health Systems is to consider the existence of false positives and false negatives in diagnoses. At the Academy, the theme of BT is exposed almost exclusively in its analytical form. With this article, the authors intend to contribute to clarify the logic behind this theorem, and get students better understanding of its important fields of application, using three methods: the classic analytical (Bayesian inference), the frequentist (frequency inference) and the numerical simulation of Monte-Carlo. Thus, it intends to explain BT on a practical and friendly way that provides understanding to students avoiding memorizing the formulas. We provide a spreadsheet that is accessible to any professor. Moreover, we highlight the methodology could be extended to other topics.