Bayesian Thinking on Different Continents
Imagine two of your friends, Lisa and John, call you during the weekend at separate times. After the second call, you got to know both weren’t feeling so well and also realized both shared similar symptoms. Lisa, who lives in the U.S expressed that, she felt feverish, has chills and headaches. She hasn’t been to the hospital yet and is wondering what might be wrong with her. John, who also called you, a couple of hours after Lisa called, only expressed that he felt “small” chills and even said it wasn’t any big deal. John lives in Nigeria.
As a concerned friend, you go ahead to google the symptoms Lisa and John told you during the phone call. Upon reading through a couple of websites, you become certain Lisa is suffering from malaria and that John was just having a bad day.
Since neither of your friends (Lisa and John) had been to the hospital yet to find out what is wrong with them, and you also aren’t a doctor, at least, what would be the possibility that Lisa truly has malaria and that John was just having a bad day?
Based on the symptoms Lisa told you, it is only logical to expect her to have malaria especially after you read and confirmed from several websites what the symptoms of someone with malaria would be. On the other hand, you most likely won’t even consider John as being sick or unwell since he shrugged off the tiny chills and even said it wasn’t any big deal.
Intuitively, this would be the way most of us would deduce the scenario. But then, we wouldn’t be fair with our deductions if we only looked at this scenario just as it appears to be.
A major piece of information we tend to forget when confronted with such a scenario is the incidence rate of diagnosing someone with malaria in the U.S? For John as well, the other major information to consider is the possibility that someone with tiny chills in Nigeria was just having a bad day.
The scenario takes a different twist when the second information is included.
The “World malaria report 2019” indicated Nigeria to have contributed to about 25% of all malaria cases worldwide, recording over 100 million malaria cases per year. The U.S records about 2,000 malaria cases per year with the majority of cases being travelers and immigrants from countries where malaria occurs. A simple ratio of this information shows that, for every single incident of malaria in the U.S, there are 50,000 more incidents in Nigeria.
This new information reveals that Lisa, whom we assumed was suffering from malaria stands a low chance of having malaria even though she expressed more symptoms of malaria. This is because the chance of diagnosing someone with malaria in the U.S especially If they aren’t travelers or immigrants from malaria-prone countries is very slim. Lisa may probably be suffering from something else other than malaria.
John, who said he had just tiny chills and expressed it wasn’t any big deal rather stands a high chance of having malaria due to the high incident rate of malaria in Nigeria. With just Nigeria contributing to about 25% of worldwide malaria cases, John is more likely to have malaria even though he expressed a single symptom of malaria.
Now, let’s imagine again, this time with John and Lisa both residing in Nigeria.
Would you say Lisa is more certain to have malaria because she exhibits more symptoms or you would say both stand an equal chance of having malaria because of the geographic location?
The scenario above highlights one of the most important theorems in conditional probabilities known as the Bayes Theorem, named after the British mathematician who lived during the 18th century, Thomas Bayes. Bayes theorem is being used to form the core tools in Artificial Intelligence and machine learning and has even found very useful applications in quantum physics and other scientific fields. Also, this framework for thinking can be used by anyone to have a more objective approach to thinking about most things in life.
If you would like to familiarize yourself with the underlying mathematical concepts of this theorem, I recommend the 3Blue1Brown channel on YouTube on this topic. Thanks for reading!