This seems to be a question about the correlation of the two over all processes that generate estimates, which seems very hard to do. Even supposing you had this correlation over processes, I’m guessing once you have a specific process in mind, you get to condition on what to know about it in a way that just screens off the prior.
In a given domain though, maybe there are useful priors one could have given what one knows about the particular process. I’ll try to think of examples.
This seems to be a question about the correlation of the two over all processes that generate estimates, which seems very hard to do. Even supposing you had this correlation over processes, I’m guessing once you have a specific process in mind, you get to condition on what to know about it in a way that just screens off the prior.
In a given domain though, maybe there are useful priors one could have given what one knows about the particular process. I’ll try to think of examples.