Shouldn’t there be some accounting of the standard deviation of your estimate of your priors? If I have a prior that I’ve reached by amounting ten bits of evidence, that is quite different from a prior that I’ve reached by amounting one bit of evidence. I don’t see how a traditionally Bayesian approach takes this into account.
Check out Metauncertainty. The post Joys of Conjugate Priors gives a specific example.
That post should be linked to more often. It is fundamental for discussions of calibration. It should have been promoted, frankly.
Thanks, I’ll read those when I get a chance.