The problem with many explanations is that people who write them have forgotten how it is to not know Bayes Theorem. Here is my humble attempt as to where peopl

The problem with many explanations is that people who write them have forgotten how it is to not know Bayes Theorem. Here is my humble attempt as to where people who want to grok Bayes theorem can start: Imagine you have been locked inside a room. You are asked what the outside weather is. Assume you have to pick one of sunny, cloudy and rainy. You know it is July so you predict it is mostly sunny. (Because intuitively you know that the odds of "sunny" is more than the other two). [1] Now you see that someone has entered the room carrying an umbrella. You are asked that question again. Of course you are going to update your answer based on the new information. Your previous odds calculation, while good, has to accommodate the umbrella factor -- a very solid piece of additional information. [2] Before the umbrella happened all you knew was [1] and it is called Prior. After you saw the umbrella the odds are conditioned on the umbrella and it is called Posterior [2]. which is what you want. And you should definitely use your intuition about the weather too [1] which now goes to the right hand side of the equation. So Posterior = ( ) x Prior This blank is called as Likelihood... it is the probability of umbrella given the weather. Imagine you live in a place where the umbrella is used only during rain. So the likelihood of an umbrella given it is sunny is very very less and is going to make the product of Prior x Likelihood very less. Whereas the likelihood of umbrella given it is rainy is almost certain. Even if your initial guess (prior) gives less odds to rain.. the product of likelihood x prior for rain is more than that of the previous paragraph product. You answer "rainy" Of course there is more to it and I suggest reading other great explanations in this thread.