Kepler Data Analysis: Non-Gaussian Noise and Fourier Gaussian Process Analysis of Stellar Variability

We develop a statistical analysis model of Kepler stellar flux data in the presence of planet transits, non-Gaussian noise, and stellar variability. We first develop a model for the Kepler noise probability distribution in the presence of outliers, which make the noise probability distribution non-Gaussian. We develop a signal likelihood analysis based on this probability distribution, in which we model the signal as a sum of the star variability and planetary transits. We argue that these components need to be modeled together if optimal signal is to be extracted from the data. For the stellar variability model we develop an optimal Gaussian process analysis using a Fourier-based Wiener filter approach, where the power spectrum is non-parametric and learned from the data. We develop high dimensional optimization of the objective function, where we jointly optimize all the model parameters, including thousands of star variability modes, and planet transit parameters. We apply the method to Kepler-90 data and show that it gives a better match to the stellar variability than the existing methods, and robustly handles noise outliers. As a consequence, the planet radii have a higher value than what the existing methods give, including splines and celerite.