Bayes' Theorem

Discuss arguments for existence of God and faith in general. Any aspect of any orientation toward religion/spirituality, as long as it is based upon a positive open to other people attitude.

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fleetmouse
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Re: Bayes' Theorem

Post by fleetmouse » Tue Nov 20, 2012 7:44 am

QuantumTroll wrote:We don't know the prior odds of the existence of God. We cannot apply Bayes' Theorem on this question, because we don't have any data about the existence of God, period. I think this is the heart of Metacrock's point, and in this he is correct.
I suspect applying these ideas directly to "the existence of God" is Meta's gloss on it, not what anyone on Carm or elsewhere said. Meta, can you link to where someone says this? I've only ever seen atheists and agnostics talk about applying Bayes to e.g. miracles and the resurrection of Jesus.
A caveat: I think the existence of God is an extraordinary claim, and my intuition says that such claims require extra convincing evidence. I agree with ECREE with regards to the existence of God, but will not use Bayes' Theorem as support for this opinion.
Here's a post where CUNY professor of philosophy Massimo Pigliucci touches on Bayes and ECREE:
A skeptic in the modern sense of the term, let’s say from Hume forward, is someone who thinks that belief in X ought to be proportional to the amount of evidence supporting X. Or, in Carl Sagan’s famous popularization of the same principle, extraordinary claims require extraordinary evidence. In that sense, then, what I will call positive skeptics do not automatically reject new claims, they weigh them according to the evidence. And of course we aren’t cynics in the modern sense of the term either, i.e. we don’t follow Groucho Marx when he famously said “Whatever it is, I’m against it!” (Of course, he was joking, though that seems to be the motto of the current Republican party.)

Now, you would think that few people would object to the pretty straightforward idea (which can actually be formalized using a Bayesian statistical framework) that one’s beliefs should be adjusted to the available evidence.
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Re: Bayes' Theorem

Post by mdsimpson92 » Tue Nov 20, 2012 9:40 am

Metacrock wrote:However, I'm hung up on the injustice of the way they do me. they are still acting like I said Bayes is stupid and wrong. what do I have sign a pledge that I support Bayes or something. It's obviously not what I think. why are they so anal retentive?
Because this is CARM and they are assholes and when you get upset you become kind of an asshole which encourages them to be even bigger assholes because they think you're being an asshole. :mrgreen:





Besides I thought we generally agreed that talking about whether God "exists" can be a bit of a non-starter depending on which concept. Particularly when dealing with a Tillichian concept of deity.
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Re: Bayes' Theorem

Post by Metacrock » Tue Nov 20, 2012 11:05 am

fleetmouse wrote:
QuantumTroll wrote:We don't know the prior odds of the existence of God. We cannot apply Bayes' Theorem on this question, because we don't have any data about the existence of God, period. I think this is the heart of Metacrock's point, and in this he is correct.
I suspect applying these ideas directly to "the existence of God" is Meta's gloss on it, not what anyone on Carm or elsewhere said. Meta, can you link to where someone says this? I've only ever seen atheists and agnostics talk about applying Bayes to e.g. miracles and the resurrection of Jesus.
A caveat: I think the existence of God is an extraordinary claim, and my intuition says that such claims require extra convincing evidence. I agree with ECREE with regards to the existence of God, but will not use Bayes' Theorem as support for this opinion.
Here's a post where CUNY professor of philosophy Massimo Pigliucci touches on Bayes and ECREE:
A skeptic in the modern sense of the term, let’s say from Hume forward, is someone who thinks that belief in X ought to be proportional to the amount of evidence supporting X. Or, in Carl Sagan’s famous popularization of the same principle, extraordinary claims require extraordinary evidence. In that sense, then, what I will call positive skeptics do not automatically reject new claims, they weigh them according to the evidence. And of course we aren’t cynics in the modern sense of the term either, i.e. we don’t follow Groucho Marx when he famously said “Whatever it is, I’m against it!” (Of course, he was joking, though that seems to be the motto of the current Republican party.)

Now, you would think that few people would object to the pretty straightforward idea (which can actually be formalized using a Bayesian statistical framework) that one’s beliefs should be adjusted to the available evidence.
http://rationallyspeaking.blogspot.ca/2 ... icism.html
why do you always assume I don't know anything? that everything I say is wrong. they said point blank that ECREE is a prefect translation of Bayes and I argue over and over there are perfect translation they contained to say "O you are Bayes you don't accept the facts of mathematics."


carm

http://forums.carm.org/vbb/showthread.p ... -idea-quot
Sylar post no 1

'ECREE' is merely an English statement of Bayes's Theorem. A claim with a low prior probability needs a higher likelihood than a claim with a high prior in order to have the same posterior. You are not only wrong, but incompetently wrong. That's it; that's ALL 'ECREE' is saying. This is a mathematical fact. You can even see a very simple proof here.

And, contrary to what Meta claims, it is use all the fracking time. For example, let's look at drug tests. Last year, an estimated 0.5% of the general US population used cocaine. Let's assume that we have a 99% accurate test for cocaine. People like Meta will try to tell you that this means that anyone who tests positive on a random drug test has a 99% chance of having actually done cocaine. The reality, however, is that if we plug the numbers into Bayes's Theorem, we see that there's nearly a 66% chance of it being a false positive.

'ECREE' is why we never do just one test for cancer. Extraordinary claims do in fact require extraordinary evidence; this is mathematical fact.

I'm not allowed to use the image tags, but here is a good cartoon about 'ECREE': http://xkcd.com/1132/



Sylor

It is a mathematical fact (see the proof linked in the OP) that claims with low priors need higher likelihoods than those with high priors to have the same posterior. That is ALL 'ECREE' is. It's merely a fashionable expression of Bayes's Theorem. Extraordinary claims (i.e., unlikely claims) require extraordinary evidence (i.e. greater than normal amount/quality of evidence).

The only goalposts that have been moved are by those who want to deny mathematical fact so that they can believe in magic.

Lance:

No ECREE is a proven fact. By Bayes theorem Pr(H|E) = Pr(E|H) * Pr(H) / Pr(E). Therefore; Pr(H|E) ≤ Pr(H) / Pr(E)

If someone means anything other than Pr(H|E) ≤ Pr(H) / Pr(E) when they talk about ECREE, then sure maybe it's a vague subjective slogan. But this is certainly true and obviously very clear.

Let's suppose that some evidence E makes hypothesis H more likely than not. Thus;

0.5 < Pr(H|E) ≤ Pr(H) / Pr(E)
0.5 < Pr(H) / Pr(E)
Pr(H) > 0.5 * Pr(E)


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And I still can't see how mathematical probability doesn't apply to miracles (eg, the resurrection). If the number of people not coming back from death by miraculous means exceeds those who do then the prior probability of a "back from death miracle" claim actually having a natural cause (and thus, being mistaken) is going to be high ... even without knowing the exact numbers.
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Re: Bayes' Theorem

Post by fleetmouse » Tue Nov 20, 2012 11:06 am

mdsimpson92 wrote:Besides I thought we generally agreed that talking about whether God "exists" can be a bit of a non-starter depending on which concept. Particularly when dealing with a Tillichian concept of deity.
Right, what we're really asking is whether being has the qualities a theist would ascribe to God over and above the qualities a naturalist would ascribe to nature.

I still think we can think about that in a Bayesian way though - by thinking of P(G|E) where G represents being having God-like qualities and E is the weight of evidence - in the broadest sense as experience, testimony and reasoning - in favor of that conception.

So P(G|E) = P(E|G) * P(G) / P(E)

So, what's the probability that we will have E given G? It depends very much on the sort of God we presume. There might well be a God of the standoffish deist sort, and all our E is purely coincidental - think of it as being like a Gettier problem where we're right (that there's a God of some sort, which is to say that being has godlike qualities) for the wrong reasons.

Now P(E) is also problematic for theism - it might be quite high given factors such as the human tendency to see agency where there is none, to invent supernatural entities (don't tell me we don't do this, it's a huge part of human culture), to tell stories to create meaning and value, etc.

So if it happens that P(E|G) is very low, and P(E) is very high, then P(G), which seems inscrutable on its own, becomes irrelevant.

Of course Bayesian reasoning of this sort is inductive so this doesn't provide a proof against God, merely makes God (i.e., that being has Godlike qualities of the sort Meta expects) improbable.

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Re: Bayes' Theorem

Post by Metacrock » Tue Nov 20, 2012 11:09 am

how are you going to assign probability to enlargement? what number do you put to mystical union when it's beyond word thought or image?

hey what's the probability that we exist? Isn't it true that something for which there is question is 0 probability? so give our existence 0 and that means it's not probable so we dont' exist right? how are you going to give God a probability if God is being itself and has to exist?


just the drive of reductionist to have only one thing in existence.e all must b eon thing, that has to be scinece.no bliss no truth no diversity no realization no saltine no enlighten just one thing my little number that make me special i can control them.

where are you getting what are you attaching them to? How can the ground of being be probabilistic? It's there it has to be there it can't not be there. the extent to which it's linked ot God is rooted in something beyond numbers or words. how you going to attack a number to something that has to be?

It can't be improbable because it's necessary but it can't be probable because there's no wave function. its' O its' real it has to be there. you can't make probably when it's certain.
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Re: Bayes' Theorem

Post by fleetmouse » Tue Nov 20, 2012 11:40 am

Where specifically does my Bayesian argument go wrong? If you follow the math you'll see that the seemingly inscrutable prior probability P(G) can vary anywhere between 0 and 1 and the argument still holds.

Bear in mind it doesn't "prove there's no God" - it merely demonstrates rational warrant for disbelief in a particular conception of God, that advanced by E.

Also bear in mind that my position is not that being doesn't exist but that being does not have Godlike qualities.

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Re: Bayes' Theorem

Post by Metacrock » Tue Nov 20, 2012 2:54 pm

fleetmouse wrote:Where specifically does my Bayesian argument go wrong? If you follow the math you'll see that the seemingly inscrutable prior probability P(G) can vary anywhere between 0 and 1 and the argument still holds.

Bear in mind it doesn't "prove there's no God" - it merely demonstrates rational warrant for disbelief in a particular conception of God, that advanced by E.

Also bear in mind that my position is not that being doesn't exist but that being does not have Godlike qualities.
I get what you are saying. In fact I am confused. I have a problem. I need run this by both you and QT.

HRG argues no one ever rises form the dead. So that in his mind means low probably that it could happen. The Lourdes article that Throwup brought up (pun intended) says the miracles they were considering can't be a miracle becuase it's happened.

so makes me ask do they (skeptics) argue the absence of other cases makes it improbable or the presence of other cases does? If a miracle is something that doesn't happen when nature is left to its own devices then the latter would be the case and other such miracle would make it improbable to be a miracle. But then it's also improbable to happen if there no other cases.
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Re: Bayes' Theorem

Post by Metacrock » Tue Nov 20, 2012 2:56 pm

It all depends upon assumptions. What's the probability of our existence? There is none. It's a certainty.
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Re: Bayes' Theorem

Post by fleetmouse » Tue Nov 20, 2012 3:57 pm

Metacrock wrote:
fleetmouse wrote:Where specifically does my Bayesian argument go wrong? If you follow the math you'll see that the seemingly inscrutable prior probability P(G) can vary anywhere between 0 and 1 and the argument still holds.

Bear in mind it doesn't "prove there's no God" - it merely demonstrates rational warrant for disbelief in a particular conception of God, that advanced by E.

Also bear in mind that my position is not that being doesn't exist but that being does not have Godlike qualities.
I get what you are saying. In fact I am confused. I have a problem. I need run this by both you and QT.

HRG argues no one ever rises form the dead. So that in his mind means low probably that it could happen. The Lourdes article that Throwup brought up (pun intended) says the miracles they were considering can't be a miracle becuase it's happened.

so makes me ask do they (skeptics) argue the absence of other cases makes it improbable or the presence of other cases does? If a miracle is something that doesn't happen when nature is left to its own devices then the latter would be the case and other such miracle would make it improbable to be a miracle. But then it's also improbable to happen if there no other cases.
Can you link me to the post where HRG says this? I need to see his exact wording and how he put it in formal terms (IF he put it in formal terms).

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Re: Bayes' Theorem

Post by fleetmouse » Tue Nov 20, 2012 4:17 pm

Metacrock wrote:It all depends upon assumptions. What's the probability of our existence? There is none. It's a certainty.
Well now, that's interesting. We're trying to determine the probability of God given the fact of "us", so...

P(G|US) = P(US|G) * P(G) / P(US)

Let's accept, as you assert, that the probability of us is a certainty. :mrgreen:

P(G) remains inscrutable. Could be anywhere between 0 and 1.

I think the crucial term here is P(US|G) - how likely is a God to create us or something very similar? How well do we think we know God? What's the likelihood that a God would have created something very different from us and our universe? I imagine you believe God has free will, so he might easily have created something else, yes? He was free to create anything at all - literally an infinity of possibilities - or nothing at all. Compound this infinity of possibilities with the fact that we're not certain, if there were a God, exactly what sort of God he would be and what his taste in universes would be like.

Let's say P(US|G) is 0.001, which is being exceedingly generous methinks given those infinite possibilities. Then the probability of a God, given the fact of us, is one in a thousand AT BEST. Probably lower, if you assign any value less than one to P(G).

Here's what it looks like with the values plugged in: p(G|US) = 0.001 * [0 to 1] / 1

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