Re: Beyond simple penalized regression

In article <emd83i$pn8$1@xxxxxxxxxxxxxxxxxxxxxxx>,
Bob O'Hara <bob.ohara@xxxxxxxxxxx> wrote:
Jerry Dallal wrote:
JS wrote:
On Dec 20, 1:41 pm, Jerry Dallal <gdal...@xxxxxxxxxxxxxxxxxxxx> wrote:
I'll *give* you computational convenience. I've always considered that
a distraction. When the Gibbs sampler and MCMC hit the collective
consciousness many thought Bayesians' problems solved since it now
became feasible to use something more flexible than a conjugate prior.
However, computational feasibility is NOT where the problem is. It's
this:

Either the prior matters or it doesn't. Well, it does.

But is assuming a prior any more dangerous than assuming linearity, or
normal residuals, or some other common artificiality.

Yes, and, unfortunately, the question is damning. Linearity, normal
residuals, and the like can be checked. "Checking a prior" is an
oxymoron. The question is damning because a prior is not something that
is "assumed". It *is*.

No, it is a model assumption. Like any model assumption, one can still
check it. One could simply choose another prior, and see if the the
results are different if the alternative prior is used.

This is a reason for investigating the amount of robustness.
This can often be done with moderate to good ease; for a
recent example which is definitely non-trivial, look at the
abstract or the more expanded version in the volume for the
last Joint Statistics Meetings by Hui Xu and myself. Do not
expect more soon; this will be his dissertation.

There ARE assumptions still to be made, but (hopefully) these
are reasonable. The prior cannot be estimated accurately,
but the procedure is a good approximation to the Bayes
procedure under a wide variety of conditions.

Bob


--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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