'Bayesian version' of the Cramer-Rao lower bound?

spunky

Super Moderator
#1
just wondering if there is some sort of "Bayesian version" of that very useful and popular result that people use in maximum likelihood, the Cramer-Rao lower bound... google seems to suggest 'no' but i just wanna double-check to see if anyone has any thoughts on the issue...
 

Dason

Ambassador to the humans
#2
What's the problem with applying the CR lower bound to a bayesian point estimate directly? http://en.wikipedia.org/wiki/Cramér–Rao_bound

And are you talking about asymptotic results? Because MLEs aren't necessarily unbiased in general and sometimes it's hard to get a closed form solution for the bias so it's pretty difficult to even use the CR lower bound for the case of MLEs sometimes.
 

spunky

Super Moderator
#3
thanks Dason! nope, i'm not saying there's anything wrong with using it with a point estimate. i'm writting chapter #1 of my thesis now and just wanted to throw out the claim that bayesian estimates can also achieve efficiency under the CR bound. but i stopped myself before writting that because, to be honest, i'm not sophisticated enough (yet) to understand the link between the inverse of the fisher info and bayesian estiamtes so i just wanted to make sure that, at least in some cases, this holds to be true so i can write it down in my thesis without the fear that someone (like the Cauchy Distribution) will come down and get me...