From lwaller@sph.emory.edu Tue May 11 13:27:20 1999
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Date: Tue, 11 May 1999 16:27:16 -0400 (EDT)
From: Lance  Waller <lwaller@sph.emory.edu>
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Subject: Re: WAPHGIS: geostatstics
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There's a good introduction to Gibbs sampling-based smoothing in the
chapter by Clayton and Bernardinelli in the Elliott et al 1992 book
(referenced in the last message).

I don't think Gibbs sampling entirely removes the problem of
oversmoothing but I'm not aware of much work quantifying this.
The fully Bayes version (based on Gibbs sampling)
does put the approach into a framework where there spatial correlation
appears as random effects (sort of spatial residuals) in a Poisson
regression model.  No Splus or SAS code, but the general method applied to
the Scotland lip cancer data from Clayton and Kaldor's Empirical Bayes
paper appears as a worked example in the BUGS (Bayesian inference Using
Gibbs Sampling) software (free software, winBUGS is the Windows version):

http://www.mrc-bsu.cam.ac.uk/bugs/Welcome.html

For some papers on constrained empirical Bayes estimation (to avoid
the overshrinkage) see the papers by Owen Devine (at CDC):

Devine, O.J., Louis, T.A., Halloran, M.E. (1994) Empirical Bayes methods
for stabilizing incidence rates before mapping.  Epidemiology. 5, 622-630.

Devine, O.J., Louis, T.A. (1994) A constrained empirical Bayes estimator
for incidence rates in areas with small populations.  Statistics in
Medicine, 13, 1119-1133.

Lance Waller


On Tue, 11 May 1999, Richard E. Hoskins wrote:

> I guess I am glad I made the crack - look at what we got! Thank you. As an
> aside I have been looking at Empirical Bayes smoothing for some time, but
> there is the apparent problem of over-shrinking which may be addressed by
> Gibbs Sampling. Any ideas? (I guess I might be more straightforward if I
> asked if there is SAS or S-Plus code available)
> 
> Again, thanks
> 
> Richard Hoskins
> rhoskins@home.com
> 
> 

.