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 survey's 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 Earth's 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.

中文翻译：

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系外行星发生率开普勒完整性和可靠性的概率方法

调查产生的系外行星目录缺乏完整性（并非每颗行星都被检测到）和可靠性不高（并非目录中的每颗行星都是真正的行星），尤其是在调查的检测极限附近。必须对基于此类目录的系外行星发生率研究的完整性和可靠性进行更正。最终的开普勒数据发布，DR25，具有经过统一审查的行星候选目录和数据产品，便于更正。我们提出了一种新的概率方法来表征开普勒完整性和可靠性，充分利用开普勒 DR25 产品。我们用泊松似然发生率方法说明了完整性和可靠性校正的影响，使用最近的恒星属性目录，该目录结合了盖亚恒星半径和对恒星群的基本统一处理。校正可靠性有显着影响：在 GK 矮星周围 20% 地球轨道周期和半径范围内的系外行星出现率，校正可靠性后为 0.015+0.011-0.007，而不校正结果为 0.034+0.018-0.012-校正为了可靠性，这种发生率降低了两倍以上。我们进一步表明，使用基于盖亚和 DR25 的恒星属性对相同的出现率有两倍的影响。我们批判性地检查了 DR25 目录和我们的发生率方法背后的假设。我们提出了几种可以提高对开普勒目录和发生率计算的信心的方法。