Research!

Well, what do ya know? Upon seeing the convergence difficulties I was having, my adviser recommended I actually look some stuff up rather than trying to figure it out on my own. Things I'll be reading up on over the next few days:

• Metropolis-Hastings MCMC - I knew about this one, but I've never read it. Not terribly surprised that it's published in Biometrika. I knew the epidemiology literature was going to be my fertile field.
• Gibbs sampling - my Bayesian text has a chapter on this, so I guess I'll be reading it sooner rather than later.
• Mixing theory - don't have any really good references here. The basic concept is straightforward (assuming you already know what a Markov process is). I think there's more to it than Wikipedia is giving credence to.

Also have a few ideas of my own to try:

• Use the seriatum nature of the data to enhance the adjacent time-series cells in the estimate.
• Use actuals as a prior and compute a posterior based on the sample.
• Combine the "block of rows at a time" concept with Metropolis-Hastings to come up with a rule for when to stay in a block versus jumping to a new block of rows.

That should keep me plenty busy until we meet again in a week.