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

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> news:6369cf9a-b2d7-4105-9c19-7196df399299@googlegroups.com...

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> Hello,

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> I am confused with the usage of Bayes with model selection.

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> I frequently see the following notation:

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> P(H | D) = P(D | H)*P(H) / P(D) where H is hypothesis and D is data.

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> It's Bayes rule. What I don't understand is the following. If in reality D ~

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> N(m,v) and my hypothesis is that D ~ (m',v) where m is different from m' and

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> if all hypothesis are equally likely

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> P(D) = sum P(D|H)*P(H)dH is not equal to true P(D), or is it?

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> =======================================================================

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> The standard notation is sloppy notation. If you use "K" to represent what

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> is known before observing data "D", then

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

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> and then go on as you were, you get

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> P(D |K) = sum P(D|H,K)*P(H|K) dH

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> ... which at least illustrates your concern.

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> "True P(D)" can be thought of as P(D | infinite pre-knowledge), while Bayes'

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> Rule requires P(D |K)=P(D |actual pre-knowledge).

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> David Jones