Bayesian Assessment of Kepler’s Small Long-Period Exoplanet Candidates with Gaussian Processes and Nested Sampling

Michael Matesic ( Université de Montréal )

There are over 5000 confirmed and validated planets beyond the Solar System to date, more than half of which were discovered by NASA's Kepler mission. The associated Kepler exoplanet catalog has only been extensively analyzed under the assumption of white noise (equal intensity on all observed timescales), 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 contaminated by this form of noise becomes increasingly difficult in lower signal-to-noise regimes, including those where Earth-Sun and Venus-Sun analog systems are expected to exist. To diagnose small long-period low-signal-to-noise targets with few (roughly 3-5) observed transit-like events (i.e. Earth/Venus-Sun analogs), we model Kepler’s photometric data as noise, treated as a Gaussian process, with and without the inclusion of a transit model. Rooted in Bayes' Theorem, nested sampling algorithms from UltraNest recover maximum a posteriori estimator parameter sets and evidences of each model, allowing for transit signatures to be dispositioned in terms of planet-candidate and false-alarm probabilities within a Bayesian framework.