Bayesian Assessment of Kepler's Candidate Exoplanets with Gaussian Processes and Nested Sampling

Michael Matesic (Bishop's University )

The Kepler exoplanet catalogue 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 coloured noise (point-to-point correlation) from stellar variability or 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 and Venus-analogues are expected to exist. To diagnose these cases, we assess candidate exoplanets by modelling Kepler’s photometric data as noise, treated as a Gaussian process, with and without the inclusion of a transit model. Nested sampling algorithms from UltraNest recover the maximum likelihood estimator parameter combinations and associated evidences of each model, allowing for true Bayesian comparison. To substantiate this methodology, results are verified against baselines established using MCMC techniques and candidates that scored highly in favour of real transits will serve as priority targets for follow-up observations from Hubble or James Webb space telescopes.