  There are more than 5000 confirmed and validated planets beyond the solar
system to date, more than half of which were discovered by NASA's Kepler
mission. The catalog of Kepler's exoplanet candidates has only been extensively
analyzed under the assumption of white noise (i.i.d. Gaussian), which breaks
down on timescales longer than a day due to correlated noise (point-to-point
correlation) from stellar variability and instrumental effects. Statistical
validation of candidate transit events becomes increasingly difficult when they
are contaminated by this form of correlated noise, especially in the
low-signal-to-noise (S/N) regimes occupied by Earth--Sun and Venus--Sun
analogs. To diagnose small long-period, low-S/N putative transit signatures
with few (roughly 3--9) observed transit-like events (e.g., Earth--Sun
analogs), we model Kepler's photometric data as noise, treated as a Gaussian
process, with and without the inclusion of a transit model. Nested sampling
algorithms from the Python UltraNest package recover model evidences and
maximum a posteriori parameter sets, allowing us to disposition transit
signatures as either planet candidates or false alarms within a Bayesian
framework.
