Statistics: Bayesian Statistics

Many times I marvel at the extent of the human capacity to think. Mr. Bayes, if you created Bayesian statistics, wow, I salute you! I don't fully understand it, as I am not very mathematically inclined, although I am always curious and amazed at the proofs that these mathematicians have.

This is the infamous 'Bayes Theorem':
1. Bayes theorem is an updating rule - you update your theory with new data.
2. An example:
Let A1 = circuits come from supplier 1 (30%); A2 = circuits from supplier 2 (50%); A3 = circuits from supplier 3 (20%).
Let E = probability that a circuit is defective.
P(E|A1) = 0.01; P(E|A2) = 0.03; P(E|A3) = 0.04.
Hence, P(A1|E) = P(E|A1)*P(A1) / [P(E|A1)*P(A1) + P(E|A2)*P(A2) + P(E|A3)*P(A3)]
= 0.01*0.03 / [(0.01*0.3) + (0.03*0.5) + (0.04*0.2)]
= 0.115.

Voila! Honestly, the wonder of Bayes theorem...