Just a short note to enquire whether anyone out there has run into
problems using the half Cauchy priors which are now commonly employed
for precisions of Gaussian distributions of random effects (and other
parameters with Gaussian priors).
We have noticed that the specification
tau<-pow(sd,-2)
sd~dunif(0,b)
b=100
(which is recommended in the the original Gelman (2006) paper and cited
extensively in examples in the WinBUGS manual)
can lead to very unstable results for uncorrelated random effects within
simple linear model specifications.
Not only is this common for simple mixed models but when b is set to
different limits in the Gaussian prior specification of the regression
parameters, then different sets of variables can be selected within
variable selection problems (such as using the approach of Dellaportas
et al (2002) or Kuo and Mallick (1998)). This seems to suggest that
there is considerable sensitivity to the specification range of the
uniform distribution on the SD.
In fact we have found that b=10 usually provides a more stable solution
and convergent sampler.
It would be interesting to find out if others have had a similar experience
Andrew Lawson
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