Mathematics – Probability
Scientific paper
Jan 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011aas...21710302j&link_type=abstract
American Astronomical Society, AAS Meeting #217, #103.02; Bulletin of the American Astronomical Society, Vol. 43, 2011
Mathematics
Probability
Scientific paper
In order for the Kepler mission to achieve its required 20 ppm photometric precision for 6.5 hr observations of 12th magnitude stars, the Presearch Data Conditioning (PDC) software component of the Kepler Science Processing Pipeline must reduce systematic errors in flux time series to the limit of stochastic noise for errors with time-scales less than three days, without smoothing or over-fitting away the transits that Kepler seeks. The current version of PDC co-trends against ancillary engineering data and Pipeline generated data using essentially a least squares (LS) approach. This approach is successful for quiet stars when all sources of systematic error have been identified. If the stars are intrinsically variable or some sources of systematic error are unknown, LS will nonetheless attempt to explain all of a given time series, not just the part the model can explain well. Negative consequences can include loss of astrophysically interesting signal, and injection of high-frequency noise into the result. As a remedy, we present a Bayesian Maximum A Posteriori (MAP) approach, in which a subset of intrinsically quiet and highly-correlated stars is used to establish the probability density function (PDF) of robust fit parameters in a diagonalized basis. The PDFs then determine a "reasonable” range for the fit parameters for all stars, and brake the runaway fitting that can distort signals and inject noise. We present a closed-form solution for Gaussian PDFs, and show examples using publically available Quarter 1 Kepler data. A companion poster (Van Cleve et al.) shows applications and discusses current work in more detail.
Kepler was selected as the 10th mission of the Discovery Program. Funding for this mission is provided by NASA, Science Mission Directorate.
Jenkins Jon Michael
Kepler Science Team
Smith Calvin J.
Twicken Joseph D.
VanCleve Jeffrey
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