Dan Foreman-Mackey (UW) crashed NYC today, surprising me, and disrupting my schedule. We began our day by arguing about the future of hierarchical modeling. His position is (sort-of) that the future is not hierarchical Bayes as it is currently done, but rather that we will be doing things that are much more ABC-like. That is, astrophysics theory is (generally) computational or simulation-based, and the data space is far too large for us to understand densities or probabilities in the data space. So we need ways to responsibly use simulations in inference. Right now the leading method is what is called (dumbly) ABC. I asked: So, are we going to do CMB component separation at the pixel level with ABC? This seems impossible at the present day, and DFM's pointed out that ABC is best when precision requirements are low. When precision requirements are high, there aren't really options that have computer simulations inside the inference loop!
Many other things happened today. I spent time with Lauren Anderson (Flatiron), validating and inspecting the output of our parallax inferences. I spent a phone call with Fed Bianco (NYU) talking about how to adapt Gaussian Processes to make models of supernovae light curves. And Foreman-Mackey and I spent time talking about linear algebra, and also this blog post, with which we more-or-less agree (though perhaps it doesn't quite capture all the elements that contribute (positively and negatively) to the LTFDFCF of astronomers!).
I think ABC is not applicable to many problems we work on - but Implicit Models might be! See https://arxiv.org/abs/1702.08896 for example...
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