Date: Feb 18, 2013 9:16 AM
Author: David Jones
Subject: Re: Trying to understand Bayes and Hypothesis
"Cagdas Ozgenc" wrote in message
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).