Bayes Rule for COVID testing
Link: https://www.theguardian.com/world/2021/apr/18/obscure-maths-bayes-theorem-reliability-covid-lateral-flow-tests-probability
Bayes Theory is a widely applied concept and is used in multiple areas such as mathematics, medicine, finance, marketing etc. It allows us to update our beliefs based on arrival of new, relevant information. The theorem was published in 1763. In the article above the author talks about the usage of Bayes’ theorem in reliability of COVID-19 tests.
In the article, the author tried to answer the question of predicting chances that you have COVID given that the test gives a false positive for every one in 1000 tests. This question is particularly important for the new LFTs(Lateral Flow Tests) that are becoming extremely common in England. The author talks about how not knowing the prior probability(the background rate in the population), can create an unnecessary scare amongst the people who don’t have COVID but are still tested positive. This is considered a misunderstanding of the Bayes’ Theorem. He concludes the article with the statement that LFTs aren’t a bad idea as long as they are followed by PCR to confirm the LFT results. He then goes on to talk about how misunderstanding of Bayes’ Theorem also causes problems in courts, and predicting if a person has cancer.
In class, we learned that Bayes’ Theorem gives us the probability of something happening given that something has already happened. The reliability of LFTs can also be decided based on Bayes’ Theorem; what’s the probability that a test is true given the probability of false positives and false negatives.