Mathematics – Probability
Scientific paper
Jan 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011aas...21714008v&link_type=abstract
American Astronomical Society, AAS Meeting #217, #140.08; Bulletin of the American Astronomical Society, Vol. 43, 2011
Mathematics
Probability
Scientific paper
In a companion talk (Jenkins et al.), we present a Bayesian Maximum A Posteriori (MAP) approach to systematic error removal in Kepler photometric data, in which a subset of intrinsically quiet and highly correlated stars is used to establish the range of "reasonable” robust fit parameters, and hence mitigate the loss of astrophysical signal and noise injection on transit time scales (<3d), which afflict Least Squares (LS) fitting. In this poster, we illustrate the concept in detail by applying MAP to publicly available Kepler data, and give an overview of its application to all Kepler data collected through June 2010. We define the correlation function between normalized, mean-removed light curves and select a subset of highly correlated stars. This ensemble of light curves can then be combined with ancillary engineering data and image motion polynomials to form a design matrix from which the principal components are extracted by reduced-rank SVD decomposition. MAP is then represented in the resulting orthonormal basis, and applied to the set of all light curves. We show that the correlation matrix after treatment is diagonal, and present diagnostics such as correlation coefficient histograms, singular value spectra, and principal component plots. We then show the benefits of MAP applied to variable stars with RR Lyrae, harmonic, chaotic, and eclipsing binary waveforms, and examine the impact of MAP on transit waveforms and detectability. After high-pass filtering the MAP output, we show that MAP does not increase noise on transit time scales, compared to LS. We conclude with a discussion of current work selecting input vectors for the design matrix, representing and numerically solving MAP for non-Gaussian probability distribution functions (PDFs), and suppressing high-frequency noise injection with Lagrange multipliers. Funding for this mission is provided by NASA, Science Mission Directorate.
Fanelli Michael N.
Jenkins Jon Michael
Smith Calvin J.
Twicken Joseph D.
Van Cleve Jeffrey E.
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