The file concerning gamma priors (180K) is at
http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/tauprior.pdf
and not the site originally given.
Ken Rice
Bugs list manager
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Dear All
Sorry to be so late in contributing to this vital discussion.
a) I agree with the discussants who point out that priors like
Gamma(0.001, 0.001) can be dangerous when used for random effects
precisions, and cannot really be claimed to be 'non-informative'
b) A number of options are available. I take the liberty of plugging a
forthcoming book (
http://www.wileyeurope.com/WileyCDA/WileyTitle/productCd-0471499757.html )
which contains a discussion of these issues. A draft of the relevant
pages can be downloaded from
http://mrc-bsu.cam.ac.uk/bugs/winbugs/tauprior.pdf
c) As others have said, if you want to make any claim as to
'non-informativeness', then you should be placing a prior directly on an
interpretable parameter. The random effects precision certainly is not
such a parameter, but the random effects standard deviation (which I shall
call tau) is.
d) The plots in the extract show that the prior on tau implied by
Gamma(0.001, 0.001) on 1/tau^2 is not, in fact, so ridiculous for random
effects logistic and Poisson models (although it may be for Normal). I
think this is the (perhaps fortuitous) reason why it has not caused too
many problems in the past.
e) My personal preference is now to use a uniform prior on tau, or a
half-normal on tau when I want to emphasise smaller values.
f) We must acknowledge that the Gamma(0.001, 0.001) prior features in many
BUGS examples and so has been taken up by many users. It was originally
used because, back in the early days of BUGS, conjugacy was a great
help. This is no longer the case and, to be completely honest, I think we
should have redone all the examples that use Gamma(0.001, 0.001) priors
before the release of WinBUGS 1.4 to check the sensitivity and see whether
a uniform on tau is OK. But I'm afraid we didn't. We certainly would like
to avoid any suggestion that this is the recommended prior.
g) Is there some generous person out there who would be willing to conduct
a class exercise to rerun all those examples with a variety of priors? The
code could be adapted from the 'prior sensitivity trick' in the 1.4
manual. If you posted up the results, you and your class could get
whatever meagre credit might be due.
david spiegelhalter
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