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 likely

P(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", then

P(H | D,K) = P(D | H,K)*P(H|K) / P(D|K)

and then go on as you were, you get

P(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