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

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




    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...
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    Re: 'Bayesian version' of the Cramer-Rao lower bound?

    What's the problem with applying the CR lower bound to a bayesian point estimate directly? http://en.wikipedia.org/wiki/Cram%C3...80%93Rao_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.
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    Re: 'Bayesian version' of the Cramer-Rao lower bound?

    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...
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    Re: 'Bayesian version' of the Cramer-Rao lower bound?


    You always need to look out for that Cauchy distribution.

    IT'LL GET YOU AND YOU BETTER LOOK OUT.
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