Bayesian Thinking And Beliefs
September 27, 2021
I am not a Maths geek, but one interesting mathematical construct that has recently fascinated me, is the Bayes theorem. About a year back, my son, who has a popular blog on Machine Learning, wrote an interesting article about Bayes Theorem. That article got me thinking about the relationship between the Bayesian model and our beliefs.
Let me share my perspective of how we all tend to process information intuitively.
Imagine a situation where you wake up one day feeling like something is wrong. You are not feeling good, and you go to a doctor. Unfortunately, the doctor is also uncertain about what is ailing you and gets you to run a battery of tests. The results come out after a week. They indicate that you have a very rare disease that affects just one in a thousand people(0.1%).
Confused and worried, you ask the doctor, “How certain is it that I have this rare disease?”
The doctor tells you that the test accuracy is 99%. The test correctly identifies that the disease is there 99 times out of a hundred. Putting it differently, one out of a hundred times, the test will return a false positive. Now listening to the doctor saying this, most of us will likely feel a surge of despair. After all, the test is 99% accurate.
Wrong. This is where Bayes Theorem comes in handy to give a more realistic perspective.
Without getting into its maths, let me present a pictorial view of the evidence we have from this example.
- One in thousand people is likely to have the rare disease. Conversely, statistically, 999 out of a thousand people are unlikely to have this rare disease.
- 99 times out of 100, the test returns a positive result. Conversely, there is a one in a hundred chance of the test result being wrong.
Let’s think of a sample size of thousand people. Now, based on our past evidence, statistically, one out of the sample of thousand people is likely to have that rare disease. So the medical test will correctly identify that person having the disease. But also, out of the other 999 people, the Medical test will return an error where ten people( 1%) would be falsely identified as having the disease. So now, if you are one of those people who has a positive test result and everyone is selected at random, then you are the only one in a group of 11 that has the disease. The probability of you having the disease is 1 in 11, which is just 9% instead of the 99% as you first surmised.
If you want to understand the maths of the Bayes Theorem, you can refer to the primer written by my son.
Relevance To Our Life
Bayesian thinking is different from a conventional way of thinking. It is driven by a probabilistic view of seeing everything around us without falling prey to intuitive and lazy thinking.
Knowing the exact mathematics of probability calculations is not as relevant in understanding Bayesian thinking. What is more important is your ability and desire to assign probabilities of truth and accuracy to anything you think you know, and then being willing to update those probabilities when new information comes in.
We all tend to get stuck with our old beliefs and assume that the world always operates the same way. And sometimes, we get caught in the web of the latest information ignoring the prior body of information. Either way, we fail to adjust for our beliefs based on the new knowledge we gain. Instead, we jump to conclusions giving more credence to some factors when we don’t have to and vice versa.
Once you start assessing situations from a Bayesian viewpoint, you become more aware that your beliefs are grayscale. You become open to adjusting your outlook and beliefs as you encounter new ideas and new evidence for and against your beliefs.
Instead of holding on to outdated beliefs by rejecting new information, you take in what comes your way through a system of evaluating probabilities.