
Re: Trying to understand Bayes and Hypothesis
Posted:
Feb 18, 2013 9:16 AM


"Cagdas Ozgenc" wrote in message news:6369cf9ab2d741059c197196df399299@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(DH)*P(H)dH is not equal to true P(D), or is it?
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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(HK) / P(DK)
and then go on as you were, you get
P(D K) = sum P(DH,K)*P(HK) dH
... which at least illustrates your concern.
"True P(D)" can be thought of as P(D  infinite preknowledge), while Bayes' Rule requires P(D K)=P(D actual preknowledge).
David Jones

