I am so interdisciplinary! I have computer-vision-meets-astronomy every Tuesday and applied-math-meets-astronomy every Wednesday. At the latter, we continued to discuss non-trivial sampling, including nested sampling with the stretch move and other methods for computing the Bayes integral. One idea we discussed was one mentioned by VanderPlas (UW) last week: Just straight-up density estimation based on a sampling followed by a mean-over-sampling of ratios between the estimated density and a product of likelihood times prior. This should (perhaps with high variance) estimate the integral (normalization). This is brilliant and simple, but we expect it won't work in very high dimensions. Maybe worth some testing though. I think VanderPlas discusses this in his forthcoming textbook.
In parallel, Foreman-Mackey has been preparing for a full assault on the Kepler data by getting ready a planet transit code. We are trying to be more general (with respect to limb darkening and the like) than the enormously useful and highly cited Mandel and Agol paper (a classic!) but without sacrificing speed. I had a brilliant insight, which is that any case of a disk blocking part of an annulus is just a difference of two cases of a disk blocking part of a disk. That insight, which could have been had by any middle-schooler, may speed our code by an order of magnitude. Hence rapid transit. Oh, have I mentioned that I crack myself up?