±66 .632 ±10% .574 ±10% .721 0.1 −0.2 ... 0.98 ±0.02 0m 03. s14 ... 3′ 14. ′′7 ... 5.38 ... 6.44 ... 5.30 ... 4.93 ... 4.69 ... 3.58 ... 2.99 ... 2.84 ... 4900.00 ... 10022 ±0.000005 − 525d ... 900.358 0.004 5.9 ±0.4 < 1.0 ... > 5 2 σ < 10 2 σ Fig. 5.— Top-left is a typical 29.4-min. LC observation of the target, for one particular frame of 62,000 exposures. The blue pixel at {400, 35} contains KIC 8639919 that is ∼2 magnitudes brighter than the target KOI-2700 located at {398.5, 35.7}. During this quarter, the target fell upon detector module 17 output node 3. Rappaport et al. (2013) ble uncertainty of ata. al. (2010). ssuming zero dilu- 00 t is being tran- y to conﬁrm, precision, that th time during ses in ﬂux are Table 1 for the hown in Fig. 6 ted ﬂux series, thin the statis- obtained from st being devel- ained with the study, though xcellent overall Fig. 6.— Epoch-folded transit proﬁle produced from PSF pho- tometry at the pixel level for KIC-2700 (blue curve) and for the nearby bright neighbor star (green curve). There is no trace of the transit in the photometry from the neighboring star. pointing & the Kepler PSF
hard way exoplanet populations physics, occurrence, formation the Kepler data noise, systematics, “de-trending” characterization parameters of individual systems
rights reserved. Printed in the U.S.A. INFERRING THE ECCENTRICITY DISTRIBUTION David W. Hogg1,2, Adam D. Myers2,3, and Jo Bovy1 logy and Particle Physics, Department of Physics, New York University, 4 Washington Place, New York, NY 10003, USA; d 2 Max-Planck-Institut f¨ ur Astronomie, K¨ onigstuhl 17, D-69117 Heidelberg, Germany 3 Department of Astronomy, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Received 2010 August 24; accepted 2010 September 25; published 2010 December 6 ABSTRACT rd maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in th e estimated eccentricity tends to be larger than the true eccentricity. As with most non-trivial observ histogram of estimated eccentricities is not a good estimate of the true eccentricity distribution. H p and test a hierarchical probabilistic method for performing the relevant meta-analysis, that is, in e eccentricity distribution, taking as input the likelihood functions for the individual star eccent plings of the posterior probability distributions for the eccentricities (under a given, uninformative ethod is a simple implementation of a hierarchical Bayesian model; it can also be seen as a k The Astrophysical Journal, 725:2166–2175, 2010 December 20 C ⃝ 2010. The American Astronomical Society. All rights reserved. Printed in the U.S.A. INFERRING THE ECCENTRICITY DISTRIBUT David W. Hogg1,2, Adam D. Myers2,3, and Jo Bov 1 Center for Cosmology and Particle Physics, Department of Physics, New York University, 4 Washington Place, 2 Max-Planck-Institut f¨ ur Astronomie, K¨ onigstuhl 17, D-69117 Heidelberg 3 Department of Astronomy, University of Illinois at Urbana-Champaign, Urbana Received 2010 August 24; accepted 2010 September 25; published 2010 D ABSTRACT Standard maximum-likelihood estimators for binary-star and exoplanet eccentricit that the estimated eccentricity tends to be larger than the true eccentricity. As with
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if you have a sampling with interim priors p ( xn | ↵ ) p ( xn | ↵0) = Z d wn p ( wn | ↵ ) p ( wn | ↵0) p ( wn | xn, ↵0) ⇡ 1 J J X j=1 p ( w (j) n | ↵ ) p ( w (j) n | ↵0)
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