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


Super Moderator
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...


Ambassador to the humans
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.


Super Moderator
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...