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On the subject of variances (or covariances), I've just looked for the
first time at the empirical covariance matrix written to the .ecm file
at the end of an MCMC run by making use of the R function <tt>readBin</tt>
described by Anders in his talk about MCMC available at <a
href="http://admb-project.org/documentation/courses/july-2009">http://admb-project.org/documentation/courses/july-2009</a>.
<br>
<br>
As noted in the previous emails, the Hessian provides good estimates in
many cases, but for those situations which seem to not be approximately
normal, I'm wondering if ADMB could be extended to allow this ECM to be
substituted for the Hessian as the basis for the jump function in MCMC.
Obviously such an option would require repeated runs of MCMC to first
estimate the ECM and then make use of it, but it seems that for some
cases, the improvement in the jump function would allow faster
convergence, especially for cases where the MCMC might jump between
alternative states that aren't well described by the Hessian. Or
perhaps I'm misinterpreting what the ECM file is or is intended for.<br>
<br>
For anyone interested, here is the R code I used to read the ECM (where
<tt>filename </tt>is a string giving the location of the .ecm file
produced by ADMB at the end of an MCMC run).<br>
<blockquote><tt># read empirical covariance file (n is upper limit on
number of values)<br>
ecmfile <- readBin(filename,what=numeric(),n=1e6)<br>
npars <- sqrt(length(ecmfile))<br>
ecm <- matrix(ecmfile,byrow=T,npars,npars)<br>
</tt></blockquote>
-Ian<br>
<br>
<br>
dave fournier wrote:
<blockquote cite="mid:4A5CB7F1.6080700@otter-rsch.com" type="cite">
<pre wrap="">Hi,
I think the title you give to this question shows that you are
thinking about it wrong. You say "ADMB estimates of variance"
which is not what they are. What they are is the use of the Hessian of
the log-likelihood to produce variance estimates. This is not an
ADMB construct but simply a standard tool to produce such estimates.
As such the ADMB estimates produced this way are just as good as any
other scheme which produces such estimates *UNLESS* they are not
calculated correctly which would make them an ADMB bug issue.
Now it is well known that the estimates provided this way are good in
the "approximately normal" situation, but they can be very bad
in other situations. That is why there are other methods such as
profile likelihoods proveded which may be more accurate in such cases.
I believe this is all discussed in the old manual.
Dave
</pre>
</blockquote>
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