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Re: Trying to understand Bayes and Hypothesis
Posted:
Feb 18, 2013 4:21 PM
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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
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