Bayes’ theorem is a term that some of you might have come across in recent times. While it is not a new concept by any means, the interest in Bayesian process has increased considerably in therecent past.
Experts believe that Bayesian ideas could be applied in a variety of different fields – from physics to cancer research, psychology, artificial intelligence, and even national security.
What is this supposedly all-encompassing theory and why is it so popular? Let us take a look.
What is Bayesian Thinking?
Bayes’ theorem deals with conditional probability. It describes the probability of an event taking place, based on the information or knowledge related to the event already available. It was first proposed by Thomas Bayes, an English clergyman and statistician, in the early 18th century and was published after his death.
The Bayesian approach towards probability is simple. You start with an estimate of the probability that a particular hypothesis is true, based on your current knowledge and the information you have about the hypothesis (commonly referred to as ‘prior’).
If you come across any new data related to it, you take it into account and then update or modify the probability based on the same. The whole process can be summed up in a simple equation as follows.
Initial Belief + New Data = New and Improved Belief.
How Does It Work?
Let us consider a cancer testing scenario.
- Let us say 1% of the general population has cancer.
- 80% of tests detect cancer accurately. In other words, 20% of tests fail to detect it even if it is there.
- 10% of tests are false positives – they detect cancer even if it is not there.
In such a scenario, let us say you test positive for cancer. Now, the question is – what are the chances you actually have the disease? Normally, you would panic and think you have cancer, since the test is 80% accurate. Let us now apply Bayesian rule to this situation.
The chances of a true positive (you have cancer and the test detected it) are 1% * 80% = 0.008.
The chances of a false positive (you do not have cancer and the results came up positive) are 99% * 10% = 0.099.
Bayesian equation says probability = expected event / all possibilities.
In this case, the expected event of getting a true positive is 0.008. The sum of all possibilities means the chance of a true positive plus the chance of a false positive (0.008 + 0.099) = 0.107. So, the probability that you actually have cancer is (0.008 / 0.107 = 0.0747), which is about 7.5%.
It might sound incredible, but it is actually true. Since the possibility of a false positive is quite high (10%), the chances of positive test results tend to drastically go down, particularly for a rare disease like cancer.
Bayes’ Theorem in Real Life
You could apply Bayesian thinking to make important decisions in your life. The important thing to remember is that the beliefs you hold and the facts you know are grayscale. When you come across new data, the beliefs could either be reinforced or rendered irrelevant and outdated, depending on whether the new evidence supports or discredits your earlier beliefs.
Once you understand the essence of Bayes’ theorem, you will no longer be stubborn about your beliefs. You will become flexible, be open to learn new things, and constantly change course based on what you learn.