Bayes’ Theorem Explained Intuitively

Bayes’ theorem is one of the most fundamental theorem in whole probability. It is simple, elegant, beautiful, very useful and most important theorem. It’s so important that there is actually one machine learning technique based on Bayes theorem named “NAIVE BAYES”.

While there are a few existing online explanations of Bayes’ Theorem, my experience is that the existing online explanations are too abstract. So in this post I will try to explain Bayes’ Theorem as intuitively as possible.

Before staring off let’s give this theorem a nickname. Whenever I learn new theorem I come up with a nickname based on the applications of that theorem. It always better to give nickname to theorems based on what they refer to. For example: Pythagoras theorem can be referred as Distance Theorem. Similarly we can refer Bays’ Theorem as Evidence theorem or trust theorem. Let’s take an example of car alarm. Your trust on car alarm updates whenever car alarm goes off. If you encounter most of the time car alarm goes off because of basketball hitting or bicycle hitting or may be any other false threat your trust goes down. Simply you are updating your trust by looking at past evidences that cause the event. Bayes’ theorem is a kind of mathematical formula that let’s you find exactly how much you should trust your evidence.

So let’s understand Bayes theorem with small example