I think your ending considerations are correct: for an evidence to be a good evidence, it needs to be something that happens with high probability in the intended model and with low probability in other models. Spiritual experiences or miracles are often better explained with naturalistic assumptions, so they are particularly bad evidence.
On the other hand, it is perfectly Bayesian to believe in something with 100% certainty and not be moved by any argument. Here on LW it’s considered bad form exactly because of this, since we believe in an imperfect brain and thus we shouldn’t limit in any way what evidence presents us with.
So, it would have to be an observation which could not possible occur except one way?
What possible piece of evidence couldn’t have, at the very least, the alternative cause of, say some super meta-God from beyond logic itself that can cause any possible observation?
Y’know. Plus a trillion other equally plausible explanations
Yes, I feel your pain. Indeed, it is unreasonable to put some evidence as pertaining exclusively to a model. But still, you believe what you want to believe, and you can start from below certainty and go up to one. I suspect also that this is what happens when people are converted by a supposed miracle and some lack of imagination.
You can’t get to it from somewhere else, if you didn’t start there. But he was saying that if you start there, you are following Bayes’ rule by refusing to change it afterwards, and that this is a good reason not to start there.
I think your ending considerations are correct: for an evidence to be a good evidence, it needs to be something that happens with high probability in the intended model and with low probability in other models. Spiritual experiences or miracles are often better explained with naturalistic assumptions, so they are particularly bad evidence.
On the other hand, it is perfectly Bayesian to believe in something with 100% certainty and not be moved by any argument. Here on LW it’s considered bad form exactly because of this, since we believe in an imperfect brain and thus we shouldn’t limit in any way what evidence presents us with.
How do you get to 100% with Bayes’?
You can with some evidence that happens only in your model and nowhere else:
P(A|E) = P(E|A)P(A) / (P(E|A)P(A) + P(E|-A)P(-A))
If P(E|A) = 1 and P(E|-A) = 0 then
P(A|E) = P(A) / P(A) = 1 (if A is not false)
Sure, this moves the problem from the evidence (P(A)) to the model (P(E|A)), but since the model is mental, you can set it anyway you want.
So, it would have to be an observation which could not possible occur except one way?
What possible piece of evidence couldn’t have, at the very least, the alternative cause of, say some super meta-God from beyond logic itself that can cause any possible observation?
Y’know. Plus a trillion other equally plausible explanations
Yes, I feel your pain. Indeed, it is unreasonable to put some evidence as pertaining exclusively to a model. But still, you believe what you want to believe, and you can start from below certainty and go up to one.
I suspect also that this is what happens when people are converted by a supposed miracle and some lack of imagination.
You can’t get to it from somewhere else, if you didn’t start there. But he was saying that if you start there, you are following Bayes’ rule by refusing to change it afterwards, and that this is a good reason not to start there.