<i>Kepler</i>Presearch Data Conditioning II - A Bayesian Approach to Systematic Error Correction

Abstract

With the unprecedented photometric precision of the Kepler Spacecraft,\nsignificant systematic and stochastic errors on transit signal levels are\nobservable in the Kepler photometric data. These errors, which include\ndiscontinuities, outliers, systematic trends and other instrumental signatures,\nobscure astrophysical signals. The Presearch Data Conditioning (PDC) module of\nthe Kepler data analysis pipeline tries to remove these errors while preserving\nplanet transits and other astrophysically interesting signals. The completely\nnew noise and stellar variability regime observed in Kepler data poses a\nsignificant problem to standard cotrending methods such as SYSREM and TFA.\nVariable stars are often of particular astrophysical interest so the\npreservation of their signals is of significant importance to the astrophysical\ncommunity. We present a Bayesian Maximum A Posteriori (MAP) approach where a\nsubset of highly correlated and quiet stars is used to generate a cotrending\nbasis vector set which is in turn used to establish a range of "reasonable"\nrobust fit parameters. These robust fit parameters are then used to generate a\nBayesian Prior and a Bayesian Posterior Probability Distribution Function (PDF)\nwhich when maximized finds the best fit that simultaneously removes systematic\neffects while reducing the signal distortion and noise injection which commonly\nafflicts simple least-squares (LS) fitting. A numerical and empirical approach\nis taken where the Bayesian Prior PDFs are generated from fits to the light\ncurve distributions themselves.\n