  We develop a statistical analysis model of Kepler star flux data in the
presence of planet transits, non-Gaussian noise, and star variability. We first
develop a model for 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 these components need to be modeled together if optimal
signal is to be extracted from the data. For the star 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 star variability
than the standard spline method, and robustly handles noise outliers. As a
consequence, the planet radii have a higher value than the standard spline
method.
