Erik Petigura (Berkeley) and collaborators found a turnover in the planet-radius distribution at small radii in this high-impact paper. They found this (more-or-less) by weighting their data samples with inverse selection probabilities. These kind of reweighted-data estimators are often unbiased but always high variance: They put the largest weights on the most marginal data. Fortunately, in the beautiful new world of exoplanets, sharing is the norm, and Petigura generously shared all of his data with Tim Morton (Princeton), Foreman-Mackey, and me. Awesome!
Today Foreman-Mackey and I pair-coded a forward model of the Petigura et al planet sample, using parameterized distribution functions, the completeness calculated by the original team, and a model for transit probability. With assumptions of independent planets (okay assumption), stationary distributions as a function of host star properties (bad assumption), negligible uncertainties (bad assumption) and separable period–radius distribution (bad assumption), it is possible to write down a fully justified likelihood function and turn the inference crank. That is, there are no real methodological freedoms. That's cool! We built and turned that crank today, also employing an iPython notebook (my first time). We got some preliminary results, which require some work to check. The thing I am excited about is that our assumptions are essentially the same as those of Petigura et al but our method is both simple and (conditionally) optimal.