Kepler Presearch Data Conditioning II - A Bayesian Approach to Systematic Error Correction

TL;DR

This paper introduces a Bayesian MAP method for Kepler data correction that effectively removes systematic errors while preserving astrophysical signals, especially variable stars, outperforming traditional cotrending techniques.

Contribution

It presents a novel Bayesian approach using priors and posterior PDFs to improve systematic error correction in Kepler photometry, maintaining astrophysical signals.

Findings

Enhanced removal of systematic errors compared to traditional methods

Better preservation of variable star signals

Reduced noise injection and signal distortion

Abstract

With the unprecedented photometric precision of the Kepler Spacecraft, significant systematic and stochastic errors on transit signal levels are observable in the Kepler photometric data. These errors, which include discontinuities, outliers, systematic trends and other instrumental signatures, obscure astrophysical signals. The Presearch Data Conditioning (PDC) module of the Kepler data analysis pipeline tries to remove these errors while preserving planet transits and other astrophysically interesting signals. The completely new noise and stellar variability regime observed in Kepler data poses a significant problem to standard cotrending methods such as SYSREM and TFA. Variable stars are often of particular astrophysical interest so the preservation of their signals is of significant importance to the astrophysical community. We present a Bayesian Maximum A Posteriori (MAP) approach where a subset of highly correlated and quiet stars is used to generate a cotrending basis vector set which is in turn used to establish a range of "reasonable" robust fit parameters. These robust fit parameters are then used to generate a Bayesian Prior and a Bayesian Posterior Probability Distribution Function (PDF) which when maximized finds the best fit that simultaneously removes systematic effects while reducing the signal distortion and noise injection which commonly afflicts simple least-squares (LS) fitting. A numerical and empirical approach is taken where the Bayesian Prior PDFs are generated from fits to the light curve distributions themselves.