Two Implications of Bayes’ Theorem

https://www.psychologytoday.com/us/blog/one-among-many/201803/two-implications-bayes-theorem 

In the spirit of finals week, I will use studying versus not studying for an exam as an example. We can infer that if you study (an “adequate” amount) there is a good chance that you will do well on the exam (P(A)). We know that if you don’t study, you may still do well on your final, but the chances of you doing well have decreased because of such (P (B)). Therefore, the probability of you doing well on your exam, given that you studied, is the chance of you studying and you not studying divided by the total chance of you not studying. If that approach of explanation was confusing, do not worry. There are a couple other approach styles, including images and a formula. This  theorem is called “Bayes’ theorem”, named after its creator Thomas Bayes.

In this article, Krueger writes about two main conclusions that can be made from this theorem. The articles describes the theorem as a description of  “how pre-existing belief (conjecture, hypothesis, or hunch) should be updated in light of new evidence (observations, data) in such a way that there are no contradictions”. Basically, this means that there would be no room for disputing results in a scenario, regardless of the various possibilities, resulting in the most accurate results possible (Krueger, Psychology Today). The two implications discussed in the article are more rooted in that of religious discovery, than math. The first implication of the theory is this, a revered (religious leader) could prove that a god does exist, but the condition necessary to do so would have to be very extreme. This means that the proof necessary would have to be undeniable, which is difficult and rare for the field of religion. The second is whether or not the hypothesis can be tested or not and not just that the data can pass tests of credibility. Because merely depending on credibility (excluding testing) can leave room for error and doubt, factors that Bayes’ theorem does not allow for.   

A possible limitation of this article is implicit bias. A prior attitude or understanding of religion in general and specifically whether or not there is a god, may have unknowingly affected the way in which certain phrasing was done. Though if so, this would have been conducted in an unconscious manner, nonetheless it would have still been evident to readers.

In my opinion, such as theory as Bayes’ is advantageous because it aims to take out as much doubt as possible. But I do not believe that 100% of doubt is ever (or rarely) able to be removed. Also, in very specific scenarios such as the testing of this hypothesis (Is there a god?) need to be handled extremely carefully, for opinions and attitudes can so easily get in the way of solely relying on testing.

A possible limitation of this article is implicit bias. A prior attitude or understanding of religion in general and specifically whether or not there is a god, may have unknowingly affected the way in which certain phrasing was done. Though if so, this would have been conducted in an unconscious manner, nonetheless it would have still been evident to readers.

In my opinion, such as theory as Bayes’ is advantageous because it aims to take out as much doubt as possible. But I do not believe that 100% of doubt is ever (or rarely) able to be removed. Also, in very specific scenarios such as the testing of this hypothesis (Is there a god?) need to be handled extremely carefully, for opinions and attitudes can so easily get in the way of solely relying on testing.