Kepler Presearch Data Conditioning II - A Bayesian Approach to Systematic Error Correction (1203.1383v1)

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.

• The paper introduces a Bayesian Maximum A Posteriori method to robustly correct systematic errors in Kepler photometric data.
• It employs specially derived cotrending basis vectors from quiet, correlated stars to minimize distortion of intrinsic stellar signals.
• This approach results in improved precision for exoplanet transit detection while preserving valuable stellar variability information.

A Bayesian Approach to Systematic Error Correction in Kepler Data

The paper "Kepler Presearch Data Conditioning II - A Bayesian Approach to Systematic Error Correction" authored by Jeffrey C. Smith et al., addresses the significant challenge of systematic error corrections in photometric data collected by the Kepler Spacecraft. This work introduces a Bayesian Maximum A Posteriori (MAP) approach to improve the cotrending procedures applied within the Kepler data analysis pipeline, mitigating systematic issues while maintaining the integrity of astrophysical signals.

Catering to the vast demand for high-precision light curves in exoplanet detection, Kepler's aim to measure the transits of Earth-size planets around Sun-like stars requires data of extraordinary precision. However, this ambition complicates processes due to observable errors in the photometric data, including discontinuities, outliers, and trends induced by the instrument itself. The Presearch Data Conditioning (PDC) module, therefore, plays a crucial role in processing these errors without obscuring vital transit signals.

The paper critiques standard cotrending methods such as SYSREM and TFA, emphasizing the need for an approach capable of retaining intrinsic stellar variability. It proposes a Bayesian MAP strategy that generates cotrending basis vectors from a subset of highly correlated and quieter stars, enabling robust fit parameter establishment over a well-defined "reasonable" range. By doing so, it enhances the accuracy of systematic effect removal beyond what is achievable through conventional least-squares fitting approaches.

The novel aspect of this research lies in its detailed numerical and empirical development of Bayesian Prior Probability Distribution Functions (PDFs). These are formed using fits to the light curve distributions themselves, which, upon maximization, yield the optimal fit that minimizes signal distortion and noise injection. The process involves technique refinements such as developing a non-standardized prior PDF shape divergent from the typical Gaussian assumption, thus aligning better with the real data distribution variances observed across Kepler's field of view.

Furthermore, this Bayesian framework refrains from constraining priors to Gaussian distributions, instead utilizing empirical distributions weighted by a metric incorporating stars' magnitude, right ascension, and declination. This detailed PDF construction ensures a more accurate representation of systematic trends, facilitating effective PCB vector weighting and fit parameter optimization.

In terms of implications, the paper presents a significant advancement in handling systematic errors in astrophysical data. It offers an improved data correction mechanism for detecting planetary transits, ultimately sharpening the precision of Kepler's mission goals. Moreover, this methodological advancement not only enhances exoplanet detection capabilities but also preserves light curve integrity for other stellar analysis domains, such as asteroseismology.

Looking forward, the paper opens avenues for further refinements in systematic error correction techniques. Expanding the framework to cater to short-cadence data or integrating hierarchical clustering to account for star clusters' localized systematic trends could potentially amplify the approach's robustness and applicability across broader astrophysical datasets.

In summary, the Bayesian approach detailed in this paper underscores the fine balance between systematic error correction and signal preservation crucial for advancing Kepler and similar missions' data utility. The methods proposed pave the way for elevated precision in both planet detection and broader star variability studies.