Date: Feb 18, 2013 4:21 PM
Author: cagdas.ozgenc@gmail.com
Subject: Re: Trying to understand Bayes and Hypothesis

Hello David,

I realized the sloppiness as well. Nevertheless philosophically I don't understand what is "actual pre-knowledge" and "infinite pre-knowlege". Could you elaborate on that? Is there a difference if my hypotheses are coming from a constrained set or from a set of all computable distributions?

Thanks



On Monday, February 18, 2013 3:16:59 PM UTC+1, David Jones wrote:
> "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