OK, this is interesting: I think our ideas of perfect Bayesians might be quite different.
They most certainly are. But it’s semantics.
I agree that #1 is part of how a perfect Bayesian thinks, if by ‘a correct prior...before you see any evidence’ you have the maximum entropy prior in mind.
Frankly, I’m not informed enough about priors commit to maxent, Kolmogorov complexity, or anything else.
I’m less sure what ‘correct posterior’ means in #2. Am I right to interpret it as saying that given a prior and a particular set of evidence for some empirical question, all perfect Bayesians should get the same posterior probability distribution after updating the prior with the evidence?
yes
There has to be a model because the model is what we use to calculate likelihoods.
aaahhh.… I changed the language of that sentence at least three times before settling on what you saw. Here’s what I probably should have posted (and what I was going to post until the last minute):
There’s no model checking because there is only one model—the correct model.
That is probably intuitively easier to grasp, but I think a bit inconsistent with my language in the rest of the post. The language is somewhat difficult here because our uncertainty is simultaneously a map and a territory.
The catch here (if I’m interpreting Gelman and Shalizi correctly) is that building a sub-model of our uncertainty into our model isn’t good enough if that sub-model gets blindsided with unmodeled uncertainty that can’t be accounted for just by juggling probability density around in our parameter space.*
For the record, I thought this sentence was perfectly clear. But I am a statistics grad student, so don’t consider me representative.
Are you asserting that this a catch for my position? Or the “never look back” approach to priors? What you are saying seems to support my argument.
OK. I agree with that insofar as agents having the same prior entails them having the same model.
aaahhh.… I changed the language of that sentence at least three times before settling on what you saw. Here’s what I probably should have posted (and what I was going to post until the last minute):
There’s no model checking because there is only one model—the correct model.
That is probably intuitively easier to grasp, but I think a bit inconsistent with my language in the rest of the post. The language is somewhat difficult here because our uncertainty is simultaneously a map and a territory.
Ah, I think I get you; a PB (perfect Bayesian) doesn’t see a need to test their model because whatever specific proposition they’re investigating implies a particular correct model.
For the record, I thought this sentence was perfectly clear. But I am a statistics grad student, so don’t consider me representative.
Yeah, I figured you wouldn’t have trouble with it since you talked about taking classes in this stuff—that footnote was intended for any lurkers who might be reading this. (I expected quite a few lurkers to be reading this given how often the Gelman and Shalizi paper’s been linked here.)
Are you asserting that this a catch for my position? Or the “never look back” approach to priors? What you are saying seems to support my argument.
It’s a catch for the latter, the PB. In reality most scientists typically don’t have a wholly unambiguous proposition worked out that they’re testing—or the proposition they are testing is actually not a good representation of the real situation.
They most certainly are. But it’s semantics.
Frankly, I’m not informed enough about priors commit to maxent, Kolmogorov complexity, or anything else.
yes
aaahhh.… I changed the language of that sentence at least three times before settling on what you saw. Here’s what I probably should have posted (and what I was going to post until the last minute):
That is probably intuitively easier to grasp, but I think a bit inconsistent with my language in the rest of the post. The language is somewhat difficult here because our uncertainty is simultaneously a map and a territory.
For the record, I thought this sentence was perfectly clear. But I am a statistics grad student, so don’t consider me representative.
Are you asserting that this a catch for my position? Or the “never look back” approach to priors? What you are saying seems to support my argument.
OK. I agree with that insofar as agents having the same prior entails them having the same model.
Ah, I think I get you; a PB (perfect Bayesian) doesn’t see a need to test their model because whatever specific proposition they’re investigating implies a particular correct model.
Yeah, I figured you wouldn’t have trouble with it since you talked about taking classes in this stuff—that footnote was intended for any lurkers who might be reading this. (I expected quite a few lurkers to be reading this given how often the Gelman and Shalizi paper’s been linked here.)
It’s a catch for the latter, the PB. In reality most scientists typically don’t have a wholly unambiguous proposition worked out that they’re testing—or the proposition they are testing is actually not a good representation of the real situation.