MCMC and model grids, stacking

For some reason these days, I keep getting asked about running MCMC in situations where the model is only defined on a discrete grid. Answer: No problem! You can either run MCMC also on that grid (with discrete proposal distributions) or else you can run MCMC in a continuous space, but snap-to-grid for the likelihood calculation (and then snap back off when you are done). Things got a bit hairier when the PHAT team (Weisz and Fouesneau are in town for a code sprint, Gordon was on the phone) were asking about the same but with non-trivial priors and exceedingly non-uniform model grids. So I decided to write down the full answer. I didn't finish by the end of the day.

It being spring break, Price-Whelan also spent a spa day down at NYU, to re-start our project on co-adding (or, really on not co-adding) imaging data. We are showing that photometric modeling (or measurement) in unstacked data beats the same in stacked data, even for sources too faint to see at any epoch. That is, you might need to stack the data in order to see the source, but you don't need to in order to detect or measure it. Worse than don't need to: You get more precision by not stacking. Duh!