A recent question on the PyMC mailing list inspired me. How can you estimate transition parameters in a compartmental model? I did a lit search for just this when I started up my generic disease modeling project two years ago. Much information, I did not find. I turned up one paper which said basically that using a Bayesian approach was a great idea and someone should try it (and I can’t even find that now!).
Part of the problem was language. I’ve since learned that micro-simulators call it “calibration” when you estimate parameter values, and there is a whole community of researchers working on “
black-box modeling plug-and-play inference” that do something similar as well. These magic phrases are incantations to the search engines that help find some relevant prior work.
But I started blazing my own path before I learned any of the right words; with PyMC, it is relatively simple. Consider the classic SIR model from mathematical epidemology. It’s a great place to start, and it’s what Jason Andrews started with on the PyMC list. I’ll show you how to formulate it for Bayesian parameter estimation in PyMC, and how to make sure your MCMC has run for long enough. Continue reading