Exoplanet catalogs produced by surveys suffer from a lack of completeness (not every planet is detected) and less than perfect reliability (not every planet in the catalog is a true planet), particularly near the surveys detection limit. Exoplanet occurrence rate studies based on such a catalog must be corrected for completeness and reliability. The final Kepler data release, DR25, features a uniformly vetted planet candidate catalog and data products that facilitate corrections. We present a new probabilistic approach to the characterization of Kepler completeness and reliability, making full use of the Kepler DR25 products. We illustrate the impact of completeness and reliability corrections with a Poisson-likelihood occurrence rate method, using a recent stellar properties catalog that incorporates Gaia stellar radii and essentially uniform treatment of the stellar population. Correcting for reliability has a significant impact: the exoplanet occurrence rate for orbital period and radius within 20% of Earths around GK dwarf stars, corrected for reliability, is 0.015+0.011-0.007, whereas not correcting results in 0.034+0.018-0.012 - correcting for reliability reduces this occurrence rate by more than a factor of two. We further show that using Gaia-based vs. DR25 stellar properties impacts the same occurrence rate by a factor of two. We critically examine the the DR25 catalog and the assumptions behind our occurrence rate method. We propose several ways in which confidence in both the Kepler catalog and occurrence rate calculations can be improved. This work provides an example of how the community can use the DR25 completeness and reliability products.
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