If we’re going to talk about how and why we should formulate priors, rather than what Bayes’ rule says, this is what we’re interested in.
But that’s not what I’m talking about. I was specifically responding to your claim that:
“prior probability”, by definition, means that we throw out all previous evidence.
So far as I can tell, that’s not part of the accepted definition. For example, Jaynes’ work on prior probabilities explicitly invokes prior information:
in two problems where we have the same prior information, we should assign the same prior probabilities.
I don’t mean to come off as a dick for nit-picking about definitions. But rigorous mathematical definitions are really important, especially if you are claiming to argue something is true by definition—and you were.
But that’s not what I’m talking about. I was specifically responding to your claim that:
So far as I can tell, that’s not part of the accepted definition. For example, Jaynes’ work on prior probabilities explicitly invokes prior information:
I don’t mean to come off as a dick for nit-picking about definitions. But rigorous mathematical definitions are really important, especially if you are claiming to argue something is true by definition—and you were.
Yes, I was wrong. I was explaining why I got so focused on the blank-slate version of the prior.
Oh, gotcha.