Its been almost ages that I had last read anything about Bayes theorem , perhaps the last time I stumbled on the theorem was when one of my friends Tarun sent a email forward with the subject line" How to choose your spouse using Bayes theorem". Though much of the article was only meant for mathematician’s world, It never occurred to me that there are a lot of commonalities between the statistical world and Bayes theorem.

Anyway , today I had to go through Bayes theorem for some work related issue:
**
Here’s a basic intro:**

Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of “Bayesian” spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. These pages will introduce the theorem and its use in the philosophy of science.

Begin by having a look at the theorem, displayed below. Then we’ll look at the notation and terminology involved.

In this formula, T stands for a theory or hypothesis that we are interested in testing, and E represents a new piece of evidence that seems to confirm or disconfirm the theory. For any proposition S, we will use P(S) to stand for our degree of belief, or “subjective probability,” that S is true. In particular, P(T) represents our best estimate of the probability of the theory we are considering, prior to consideration of the new piece of evidence. It is known as the prior probability of T.

What we want to discover is the probability that T is true supposing that our new piece of evidence is true. This is a conditional probability, the probability that one proposition is true provided that another proposition is true.

My thoughts:
At the core of bayes theorem lies the fact of testing a hypothesis ,given a piece of new evidence. It will not change the original hypothesis by a large amount, but only slides it down or up depending on the evidence. Over a period of time, we see that initial bias of the assumption gets evened out.

Links :
Intro to Bayes theorem
Intuituve expanation of Bayes Theorem