In regards to Stefan Van Dongen's issue about non-convergence, I must say that I
have the same problem with the linear coefficients of fully bayesian generalized
linear models. My application is somewhat different than Stefan's, as I use
WINBUGS for Poisson regression to smooth diease rates in small area maps and to
assess the effect of covariates. For smoothing, there is never a problem, as I
get rapid convergence of the predicted diease counts; however, for linear terms,
I can not obtain convergence and therefore can not draw any defensible inference
about these terms. I usually run 3 independent chains, where initial values for
the linear terms are chosen based on preliminary maximum likelihood analysis (or
pseudo ML). Initial values are chosen to represent the MLE estimate and +/- 4
standard errors in order to represent over-dispersed initial values, but not
wildly over-dispersed.
As with Stefan, I have also experimented with more informative priors. This
sometimes leads to "apparent" convergence, but it does not hold as one continues
to run the chain.
I have discovered through conversation that others experience this same problem.
Perhaps, however, this should not be a surprise since Eberly and Carlin
(Statistics in Medicine 2000; 19:2279-2294) point out that this may be related
to problems with model identifiability. I use the convolution prior discussed
by Eberly and Carlin, where two variance component are included--a spatially
structured and unstructured one; however, I continue to have problems with
convergence of the linear coefficients even if I proceed with only one variance
component (either structured or not).
I have always felt that some of the best guidance that us "users" need from
those more knowledgeable in full bayes analysis is in the selection of initial
values and priors. However, this particular problem of non-convergence of
linear coefficients in GLM's may simply be unsolvable. If interest lies with
smoothing, they work beautifully; however, if interest lies with quantifying the
strength of covariate effects, then a non-Bayesian approach, such as pseudo-MLE
may be necessary (or perhaps Empirical Bayes). Perhaps these considerations also
apply to Stefan's problem.
Sincerely,
Glen Johnson
__________________
Glen D. Johnson, PhD
New York State Department of Health
Bureau of Environmental and Occupational Epidemiology
Flanigan Square, 547 River Street, Room 200
Troy, NY 12180-2216 USA
Phone: 518-402-7950 Fax: 518-402-7959
email: [log in to unmask]
---------------------- Forwarded by Glen D. Johnson/BEOE/DOHEE/CEH/OPH/DOH on
03/14/2001 09:37 AM ---------------------------
Stefan Van Dongen <[log in to unmask]> on 03/14/2001 09:21:50 AM
Please respond to Stefan Van Dongen <[log in to unmask]>
To: [log in to unmask]
cc: (bcc: Glen D. Johnson/BEOE/DOHEE/CEH/OPH/DOH)
Subject: informative priors to improve convergence behaviour
Hi all,
I am currently running a latent variable model and often encounter
convergence problems when sample sizes are relatively small. This
manifests itself when individual chains completely 'run off' to values
that are no longer biologically meaningfull. I am thinking of using
informative priors to 'bound' the chains a bit, and would like to hear
from you what your experiences are with that in terms of sensitivity of
the outcome and how to approach this in an 'almost objective' way
thanks a lot
Stefan
--
Dr. Stefan Van Dongen
Group of Animal Ecology
Department of Biology
University of Antwerp
Universiteitsplein 1
B-2610 Wilrijk, Belgium
Tel: + 32 (0)3 820 22 61
Fax: + 32 (0)3 820 22 71
Email: [log in to unmask]
URL: http://bio-www.uia.ac.be/u/svdongen/index.html
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