[Developers] MCMC in ADMB

[Cole Monnahan]

Hi ADMB developers,

We're grad students at the University of Washington and we've been looking
through the source code to better understand how MCMC is implemented in
ADMB. I started doing this because I wanted to specify an arbitrary
covariance matrix, but Jim Ianelli encouraged me to explore some of the
algorithms for the other available options. I couldn't find documentation
for them, so I began writing them up with the idea of putting them into the
ADMB manual. As time went on it grew more from a technical description to a
starting place for users who had never used ADMB for Bayesian analyses
before (as we were). So we're calling it a "guide" for lack of a better
term. Our intent, as recommended by Jim, is to put it on the ADMB website,
probably in a similar place to my other short write-up about the bounding
functions
<http://www.admb-project.org/examples/admb-tricks/covariance-calculations>.

In doing this work we developed a list of updates we think would be
worthwhile to include in future versions. We're not experienced C++
programmers, but we would be happy to work with someone to help implement
those into the source.

Some proposed ideas for changes:

   - Set mcsave default to 1, current default is to save nothing which
   would be unexpected for a lot of users.
   - Warn users if mcsave is invoked with the hybrid method (it has no
   effect).
   - Create new output file similar to .hst that outputs useful information
   of the analysis (mcmc options used, time started, ended, acceptance ratios,
   final scaling factor, etc.).
   - Another file similiar to the .psv file (which contains only
   parameters) that stores the draws of sd_report variables.
   - Remove need for a sdreport variable for MCMC (checked with Dave, not
   needed).
   - Use a random seed if none is provided by user, or at least warn user
   of the default which is to use the same seed value (36519). In practice
   most users are reusing the same seed across models -- maybe not a good idea
   except for reproducibility which could be done by looking at the seed in
   the .hst file.
   - Clean up the console output for both Metropolis and hybrid runs.

So please have a quick look through and let us know if (1) you find
anything incorrect, and (2) whether you think it should be added into the
ADMB manual or left as a separate document.

Thanks,
Cole, Melissa, and Peter
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