Dear BUGS users,
Many thanks to those who respond to my question about the use of
dgamma(0.001,0.001) for a uninformative prior on a precision
parameter. Below is my original question and the summary of the responses.
The main feature seems to be the Pandora's Box of Bayesian analysis :
As highlighted by William Bell ([log in to unmask]), using the Gamma(eps,eps)
for the precision, where eps is a small
number like .001, results in priors for both the precision and the variance
that may be highly informative.
Indeed, the resulting prior (for both variance and precision) peak at zero,
drop sharply, and then are relatively flat. This is not a problem if the
likelihood peaks away from zero, but if, unfortunatly, the likelihood for
the variance peaks at zero, the posterior for the variance also will peak
at zero.
This is not what is intended and it could make the sampling in the full
conditional distribution of the variance impossible (or the precision).
I didn't received any response to the question "why does WinBUGS 1.4 trash
when the1.3 version runs".
-------------------------------------------------------
MY ORIGINAL QUESTION :
A commonly used "non informative prior" for a normal variance is
tau ~ dgamma(0.001,0.001)
I believe the reason is that a gamma pdf approximates an inverse
distribution when parameters are taken very small.
The problem :
I have a model with such a prior
tau ~ dgamma(0.001,0.001) ;
var <- 1/tau ;
on the precision, which is running without any problem under WinBUGS13. But
this model doesn't run under the updated version WinBUGS14 (trap message :
"unable to bracket slice for node tau").
My questions :
1) Does the updated 1.4 version use other sampling methods as 1.3 ?.
2) The model is running under 1.4 with the following code :
var ~ dgamma(0.001,0.001) ;
tau ~ 1/var ;
To my mind, assigning a prior pdf =1/V on the Variance V is the same than
assigning a prior pdf =1/Tau on the precision Tau. Thus, is this second
solution wrong ?.
3) Is it better to use something like
log.tau ~ dunif(-10,10) ;
tau <- exp(log.tau) ?
RESPONSES :
------------------------------------------------------------------
William Bell ([log in to unmask])
One comment: You may already realize this, but you need to be careful
about using the Gamma(eps,eps) for the precision, where eps is a small
number like .001. The resulting priors for both the precision and the
variance peak at zero, drop sharply, and then are relatively flat. This
is
fine if the likelihood peaks away from zero, but with variance
components
sometimes the likelihood for a variance peaks at zero, and when this
happens with the aforementioned prior the posterior for the variance
will also lump up at zero. In this case, the prior is actually very
informative,
which is not what is intended.
---------------------------------------------------------------
Dongwoo Kang ([log in to unmask])
My experience suggests using tau ~ dgamma(0.01,0.01) or dgamma(0.1,0.1) to
avoid
numerical overflow problem, since dgamma(0.001,0.001) can produce very small
numbers. I would also like to hear about opinions on 3). Thanks.
--------------------------------------------------------------
Kaul, Sanjay M.D. ([log in to unmask])
Doesn't the commonly used 'non-informative prior' in WINBUGS negate the very
essence of Bayesian Philosophy of integrating prior knowledge with current
data? I look forward to the responses. Many thanks
------------------------------------------------------------------
Etienne RIVOT
*********************************************************************
Etudiant en these / Ph.D. Student
UMR Ecobiologie et Qualite des Hydrosystemes continentaux
Institut National de la Recherche Agronomique
65, rue de St Brieuc, CS 84215, 35042 Rennes cedex, FRANCE
Tel : +33 2 23 48 54 49 ; Fax : +33 2 23 48 54 40
Email : [log in to unmask]
Internet : http://www.rennes.inra.fr/
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