Symptoms and Probabilities: Bayes’ Theorem Helps With Hypochondria
Is it just a normal headache, or something far, far, worse, like a ruptured brain aneurysm? Is it just some difficulty breathing, or a sign of secondary drowning? These kinds of questions plague me frequently, drowning me deep within a sea of worry and despair. Yet every time, without fail, my fears never come to fruition.
I never seem to learn from these experiences, always submerging back into the endless queries on symptoms and treatments, causing undue stress and panic, and hurting more than the symptoms they were caused by. I knew I needed a way out of this cycle, or at least a way to cope, to overcome these fears. Fortunately, Liv Boeree, a professional poker player, provides a solution: Bayes’ Theorem.
This coping method may not work for everyone, but it does help to assuage my fears. Personally, the root cause of these fearful presumptions is the absolute certainty, at least within my mind, that these symptoms are a sign of a terrible illness/condition. As such, putting the probabilities in perspective really helps.
For example, let’s look at what Bayes’ Theorem says about headaches and a brain aneurysm. According to the theorem, the probability of A given B is equal to the probability of B given A times the probability of A by itself divided by the probability of B by itself. In this example, A would mean you have a ruptured brain aneurysm, while B would mean you have a headache. It’s a bit hard to get the exact probabilities for this, but an estimate of the probability’s magnitude will do just fine.
According to the Brain Aneurysm Foundation, the annual rate of rupture for a brain aneurysm is 8-10/100,000. We can take the middle of the two and say that the probability is .00009. Let’s assume that if you have a brain aneurysm, you will also have a headache. We’ll estimate that the likelihood of having a headache without a brain aneurysm is somewhat low, but not too much, such as .04. We can plug this into Bayes’ Theorem, resulting in a probability of .00225, or 0.225%
Although there’s still no guarantee that it’s just a typical headache, and the probabilities are a bit lacking of a case-by-case basis, it helps. Just the realization that your mind is skewing the likelihood out of your favor helps to relieve some concerns. And if it helped me, it very well might help someone else too.
Sources:
https://www.vox.com/future-perfect/2018/11/30/18096751/bayes-theorem-rule-rationality-reason