Thomas Bayes, an eighteenth-century English statistician, published just two works in his career (and one of them was on theology). His name may still sound familiar, despite producing relatively fewer papers than many of his counterparts of the 1700s. Nonetheless, Bayes is one of the most well-known figures in the history of mathematics, thanks to formulating the special case of the appropriately named Bayes Theorem. (https://beautifulequations.co.uk/collections/bayes-theorem)
Don’t be afraid of these strange symbols! Put simply, P(A|B) represents the probability of some event A, given that another event B has already occurred and P(A) or P(B) is the probability of event ‘A’ or ‘B’ happening independently.
Most mathematicians are no stranger to this neat formula. It’s a fundamental part of probability and a useful tool whenever tackling a problem that involves some conditional probability. However, like most mathematics, its applications extend far beyond theory. Here are 3 ways Bayes’ theorem appears in the world!
1. False Negative Test Results
Somehow Covid always seems to be involved… Bayes’ theorem is important in validating results in testing, including virus testing – when a positive test result does not definitely mean that someone has the virus. If ‘A’ is the event of testing positive and ‘B’ is the event of having the virus, then P(A|B), the probability you test positive given you have the virus is a very important measure. If P(A|B) is not very close to 1 then the test will miss positive cases. Clearly in the case of Coronavirus this could be very dangerous!
2. Internet Dating
Maths isn’t exactly the language of love but we do use it subconsciously when searching for a potential partner. Everyone has certain preferences; say you love country music and you’re sure that if a date shared this passion then they would instantly become more attractive. Letting ‘A’ be the event of a successful date and ‘B’ being said country fan, then thanks to Bayes you could estimate the increased probability of a successful date given this key feature. In today’s world of Tinder and Bumble, these ‘hunches’ and calculations we make without necessarily being aware of them are literally coded into the apps’ software!
3. Do you need your umbrella?
You are about to leave for work and see an ominous cloud looming in the distance. But do you take your umbrella? That quick thought process that runs through your head of the likelihood of rain is again an application of Bayes’ theorem. This scenario is slightly simpler. As it’s impossible to have rain without clouds, if ‘A’ represents rain and ‘B’ clouds then P(B|A), the probability of clouds given rain, must be equal to 1. Therefore, in estimating P(A|B) the probability of rain given it’s cloudy (and hence also the probability you’ll need your umbrella) becomes P(A)/P(B). You’ve combined your own observations with Bayes’ theorem to make a more informed decision! (However it’s probably best to take your umbrella regardless…)