I spent the weekend and today working on my hierarchical exoplanet papers. Today, Bovy pointed out that they are really just more general versions of our extreme deconvolution method for forward-modeling noisy (and heteroscedastic) data. (On that note, Bovy just resubmitted the paper to JOAS.) Because I care—by assumption—only about the distribution function, and not about improving the individual-exoplanet measurements, I am not doing anything properly hierarchical. I think he is right; that adjusts my introduction.
Zolotov and I discussed the issue that any cusp in the projected phase space distribution function will have finite thickness, which smooths out the infinities. We talked about methods for computing the cusp function safely. Power laws are difficult.