Simple Explanation of Bayesian Logic
physcab: I always like to think of an application when learning new concepts.  Bayesian theory is often used in machine learning, for example, where the "learning" is simply done by updating a bayesian equation.  In ML you often have this:posterior probability = conditional probability * marginal probability.where,marginal prob is an initial guess (ie you have two boxes and the probability of choosing one is 5/10)conditional probability is typically an observation given the marginal (ie you look inside one of the boxes and there are 4 red balls and 2 green balls, so the probability of a red ball in box 1 is 4/6 or 2/3.)posterior is the simply the probability of those two multiplied together (ie 2/3 * 1/2 = 1/3).Now, in ML, because of a property called conjugacy...you can use this posterior probability to update the learning process.  In the next iteration, you would use 1/3 as your initial marginal prob guess.If you're looking for good tutorials, I would suggest:Paul Graham's Spam Bayes filter:http://www.paulgraham.com/better.htmlAndrew Moore's Statistical learning tutorials:http://www.autonlab.org/tutorials/Christopher Bishop's Pattern Recognition and Machine Learning- Chapter 1: Probability Theoryhttp://research.microsoft.com/en-us/um/people/cmbishop/prml/...