By a nice coincidence I noticed this paper on astro ph yesterday by Lee et al. presenting a relatively straightforwards model for photon counting statistics which happens to use the device of generating functions to find analytically the likelihood function as a sum of various component sources—and which in turn might have a natural extension via the Russian Roulette version of pseudo-marginal MCMC (e.g. Lyne et al. 2014) highlighted in my recent talk at the RAS Gravitational Wave meeting (see link to slides below). In the Lee et al. paper the infinite series summation defining their likelihood function is able to be analytically solved for the basic model, but this tractability is not anticipated to hold for more complex versions; hence my expectation is that the Russian Roulette method for creating an unbiased Monte Carlo estimate of the series summation with only a (random) finite number of terms could well provide a solution amenable to posterior sampling with pseudo-marginal MCMC. Anyway, the talk slides:

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Nice talk, sorry to have missed it, but thanks for posting the slides.

However: “IMHO, 90% of astrostatistics problem can be solved within hours (at most, a day) but writing the model out in hierarchical form and coding it up in STAN/JAGS”

Well, no. The likelihood is typically more complex (often involving numerical simulation and/or computation) than can be built with relatively simple analytical building blocks as available in STAN/JAGS! In some cases it’s non-differentiable and this kills STAN.

JAGS really only works for the simplest astrostats problems, not “most”.