```Date: Feb 18, 2013 9:16 AM
Author: David Jones
Subject: Re: Trying to understand Bayes and Hypothesis

"Cagdas Ozgenc"  wrote in message news:6369cf9a-b2d7-4105-9c19-7196df399299@googlegroups.com...Hello,I am confused with the usage of Bayes with model selection.I frequently see the following notation:P(H | D) = P(D | H)*P(H) / P(D) where H is hypothesis and D is data.It's Bayes rule. What I don't understand is the following. If in reality D ~ N(m,v) and my hypothesis is that D ~ (m',v) where m is different from m' and if all hypothesis are equally likelyP(D) = sum P(D|H)*P(H)dH is not equal to true P(D), or is it?=======================================================================The standard notation is sloppy notation. If you use "K" to represent what is known before observing data "D", thenP(H | D,K) = P(D | H,K)*P(H|K) / P(D|K)and then go on as you were, you getP(D |K) = sum P(D|H,K)*P(H|K) dH... which at least illustrates your concern."True P(D)" can be thought of as P(D | infinite pre-knowledge), while Bayes' Rule requires  P(D |K)=P(D |actual pre-knowledge).David Jones
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