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We characterize the occurrence rate of planets, ranging in size from 0.5-16R$_\oplus$, orbiting FGK stars with orbital periods from 0.5-500 days. Ouranalysis is based on results from the "DR25" catalog of planet candidatesproduced by NASA's Kepler mission and stellar radii from Gaia "DR2". Weincorporate additional Kepler data products to accurately characterize theefficiency of planets being recognized as a "threshold crossing events" (TCE)by Kepler's Transiting Planet Search pipeline and labeled as a planet candidateby the robovetter. Using a hierarchical Bayesian model, we derive planetoccurrence rates for a wide range of planet sizes and orbital periods. Forplanets with sizes $0.75-1.5$ R$_\oplus$ and orbital periods of 237-500 days,we find a rate of planets per FGK star of $<0.27$ ($84.13$th percentile). Whilethe true rate of such planets could be lower by a factor of $\sim~2$ (primarilydue to potential contamination of planet candidates by false alarms), the upperlimits on the occurrence rate of such planets are robust to $\sim~10\%$. Werecommend that mission concepts aiming to characterize potentially rockyplanets in or near the habitable zone of sun-like stars prepare compellingscience programs that would be robust for a true rate in the range $f_{R,P} = $$0.03-0.40$ for $0.75-1.5$ R$_\oplus$ planets with orbital periods in 237-500days, or a differential rate of $\Gamma_\oplus \equiv (d^2 f)/[d(\ln P)~d(\lnR_{p})] = $ $0.06-0.76$.

Occurrence Rates of Planets orbiting FGK Stars: Combining Kepler DR25, Gaia DR2 and Bayesian Inference