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:
http://rationallyspeaking.blogspot.ca/2 ... icism.html
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.
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."
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/
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.
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)
Darth Pringle View Post
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.