We infer the number of planets-per-star as a function of orbital period and planet size using Kepler archival data products with updated stellar properties from the Gaia Data Release 2.  Using hierarchical Bayesian modeling and Hamiltonian Monte Carlo, we incorporate planet radius uncertainties into an inhomogeneous Poisson point process model.  We demonstrate that this model captures the general features of the outcome of the planet formation process around GK stars, and provides an infrastructure to use the Kepler results to constrain analytic planet distribution models.  

 

We report an increased mean and variance in the marginal posterior distributions for the number of planets per GK star when including planet radius measurement uncertainties.  We estimate the number of planets-per-GK star between 0.75 and 2.5 R_Earth and 50 to 300 day orbital periods to have a 68% credible interval of 0.49 to 0.77 and a posterior mean of 0.63. This posterior has a smaller mean and a larger variance than the occurrence rate calculated in this work and in Burke et al. 2015 for the same parameter space using the Q1-Q16 (previous Kepler planet candidate and stellar catalog), and a larger mean and variance than when using the DR25 (latest Kepler planet candidate and stellar catalog).  We find that the accuracy and precision of our hierarchical Bayesian model posterior distributions are less sensitive to the total number of planets in the sample, and more so on the characteristics of the catalog completeness and reliability and the span of the planet parameter space.