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There are more than 5000 confirmed and validated planets beyond the solarsystem to date, more than half of which were discovered by NASA's Keplermission. The catalog of Kepler's exoplanet candidates has only been extensivelyanalyzed under the assumption of white noise (i.i.d. Gaussian), which breaksdown on timescales longer than a day due to correlated noise (point-to-pointcorrelation) from stellar variability and instrumental effects. Statisticalvalidation of candidate transit events becomes increasingly difficult when theyare contaminated by this form of correlated noise, especially in thelow-signal-to-noise (S/N) regimes occupied by Earth--Sun and Venus--Sunanalogs. To diagnose small long-period, low-S/N putative transit signatureswith few (roughly 3--9) observed transit-like events (e.g., Earth--Sunanalogs), we model Kepler's photometric data as noise, treated as a Gaussianprocess, with and without the inclusion of a transit model. Nested samplingalgorithms from the Python UltraNest package recover model evidences andmaximum a posteriori parameter sets, allowing us to disposition transitsignatures as either planet candidates or false alarms within a Bayesianframework.

Gaussian Processes and Nested Sampling Applied to Kepler's Small Long-period Exoplanet Candidates