ABC, IMF, and habitability

While Foreman-Mackey and Barclay set off on a tangent to measure (or limit) exoplanet masses using n-body models of exoplanet systems observed by Kepler, I had a great phone call with Schaefer (CMU), Cisewski (CMU), Weller (CMU), and Lang about using Approximate Bayesian Computation (ABC) to ask questions about the universality of the high-mass initial mass function (IMF) in stellar clusters observed in the PHAT survey. The idea behind ABC is to do a kind of rejection sampling from the prior to make an approximation to posterior sampling in problems where it is possible to generate data sets from the model (and priors) but impractical or impossible to write down a likelihood function.

The reason we got this conversation started is that way back when we were writing Weisz et al on IMF inference, we realized that some of the ideas about how high-mass stars might form in molecular clouds (and thereby affect the formation of other less-massive stars) could be written down as a data-generating process but not as a computable likelihood function. That is, we had a perfect example for ABC. We didn't do anything about it from there, but maybe a project will start up on this. I think there might be quite a few places in astrophysics where we can generate data with a mechanistic model (a simulation or a semi-analytic model) but we don't have an explicit likelihood anywhere.

At the end of the day, Sarah Ballard (UW) gave a great Physics Colloquium on habitable exoplanets and asteroseismology, and how these two fields are related. They are related because you only know the properties of the exoplanet as well as you can understand the properties of the star, and asteroseismology rocks the latter. She mentioned anthropics momentarily, which reminded me that we should be thinking about this: The anthropic argument in exoplanet research is easier to formulate and think about than it is in cosmology, but figuring it out on the easier problem might help with the harder one.