Re: BAYESIAN (weighted) PROBABILITY ??
From: George Hammond (research137_at_hotmail.com)
Date: 07/26/04
- Next message: Richard Ulrich: "Re: Derivation of AIC"
- Previous message: George Hammond: "Re: BAYESIAN (weighted) PROBABILITY ??"
- In reply to: Goran Dhemmeog: "Re: BAYESIAN (weighted) PROBABILITY ??"
- Messages sorted by: [ date ] [ thread ]
Date: Mon, 26 Jul 2004 14:07:31 GMT
"Goran Dhemmeog" <hcraeser731@hotmail.com> wrote in message
news:b9eccd47.0407232212.535d50d9@posting.google.com...
> 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.
[Hammond]
the previous poster "Henry" has already pointed out that the
liklihood ratio actually already contains the weights. So, you're
right, the answer is no, one doesn't have to put in "weights" separately.
In fact... one implicitly considers the weights when one decides
(estimates) the liklihood ratio.
Anyway.. I am going to attempt a calculation of the "probablility
that GOD=G_uv is CORRECT, given the scientific evidence". I'll be posting
it on sci.physics.relativity when i get around to it... you can
give me your reaction then.
-- ============================================ SCIENTIFIC PROOF OF GOD WEBSITE http://geocities.com/scientific_proof_of_god mirror site: http://proof-of-god.freewebsitehosting.com ============================================
- Next message: Richard Ulrich: "Re: Derivation of AIC"
- Previous message: George Hammond: "Re: BAYESIAN (weighted) PROBABILITY ??"
- In reply to: Goran Dhemmeog: "Re: BAYESIAN (weighted) PROBABILITY ??"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
|
