Re: BAYESIAN (weighted) PROBABILITY ??
From: Goran Dhemmeog (hcraeser731_at_hotmail.com)
Date: 07/24/04
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Date: 23 Jul 2004 23:12:15 -0700
You are asking? Are you not as omniscient as you claim to be? Dare I a
humble no-one say anything?
I said before: I do not understand the formulas you give. I do not
have to book, but you say you do. Try to follow now. Let us denote
with G the random variable that god exists (G=1 god exists, G=0 does
not). Also there are then 6 random variables, E1, E2, ..., E6,
attaining also boolean values (which are here chosen all 1s. All 6
events described occured), that are assumed dependent on the
exisistence of God. Then the official Bayes's formula for the
posterior probability is:
P(G'=1|E1=1,E2=1,...,E6=1) =
P(G=1)\prod_{i=1}^6{P(Ei=1|G=1)}
-----------------------------------------------------------------,
P(G=1)\prod_{i=1}^6{P(Ei=1|G=1)} + P(G=0)\prod_{i=1}^6{P(Ei=1|G=0)}
where P(G=1) is the prior probability. I write it as a product so that
no-one confuses with the iteration. Now the prior can be set quite
well to 1/2 (god is a priori equally like to exist or not). I do not
quite understand the functions P(Ei=1|G=1) and P(Ei=1|G=0). Look from
the book what there corresponds to these?
The answer to your question is no. There is no need for weights since
the probabilities are already assigned arbitrarily. Although there is
this a little unofficial method: raise them to powers. Replace in the
formula above P(Ei=1|G=1) with P(Ei=1|G=1)^ai and P(Ei=1|G=0) with
P(Ei=1|G=0)^ai, where ai is the (arbitrary) weight exponent, ai>0.
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