Foreman-Mackey and I pair-wrote some more in his exoplanet populations paper. We made strict (and explicit) definitions of "rate" and "rate density" and audited the document to be consistent with those definitions. A rate is a dimensionless expectation value for an integer draw from a Poisson distribution. A rate density is something that needs to be integrated over a finite volume in some parameter space to produce a rate. We reminded ourselves that the model is an "inhomogeneous Poisson process" (inhomogeneous because the rate density varies with planet period and radius) and said so where appropriate. We massaged the text around the issues of converting rate estimates from other projects into rate densities to compare with our results. And we finished the figure captions. So close. I also wrote a bit in my own Atlas.
[Added after the fact: Above I am talking about the "rate" of a process inside a discrete population: This is about the rate at which planets host stars. There is another use of "rate" in physics that is number per time; it has to be integrated over a time interval to get a dimensionless number. The words "rate" and "frequency" both have these double meanings of either dimensionless object (in discrete probability contexts) or else number per time (in time-domain physics contexts).]