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.
Highlights
IntroductionBayes' Theorem (alternatively Bayes' law or Bayes' rule) has played since 18th century
Bayes' Theorem has played since 18th century
It is demonstrated throughout this article that a theorem with a complicated statement, and an even more complicated mathematical representation, can be described in a simpler way using pure logic through two methods: the frequentist and the numerical simulation – the later even more intuitive than the former
Summary
Bayes' Theorem (alternatively Bayes' law or Bayes' rule) has played since 18th century. It refers to a mathematical formula used to calculate the probability of an event based on the data about another event that has already occurred, which is called conditional probability (Joyce 2021). In the domain of scientific knowledge disciplines, such as Physics and Chemistry, the first studies were essentially experimental, and the observed effects were later explained with the support of mathematical logic (Jeffreys 1973). The experiences carried out by its precursors are routinely reproduced in the laboratories of academic institutions, to provide students with a better understanding of the phenomena and their laws that those disciplines develop (Daveedu Raju et al 2019). In the field of Statistics, experimentation in academic
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