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Bayesian estimates of astronomical time delays between gravitationally lensed stochastic light curves

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Title: Bayesian estimates of astronomical time delays between gravitationally lensed stochastic light curves
Authors: Tak, H
Mandel, K
Van Dyk, DA
Kashyap, V
Meng, XL
Siemiginowska, A
Item Type: Journal Article
Abstract: The gravitational field of a galaxy can act as a lens and deflect the light emitted by a more distant object such as a quasar. Strong gravitational lensing causes multiple images of the same quasar to ap- pear in the sky. Since the light in each gravitationally lensed image traverses a different path length from the quasar to the Earth, fluc- tuations in the source brightness are observed in the several images at different times. The time delay between these fluctuations can be used to constrain cosmological parameters and can be inferred from the time series of brightness data or light curves of each image. To estimate the time delay, we construct a model based on a state- space representation for irregularly observed time series generated by a latent continuous-time Ornstein-Uhlenbeck process. We account for microlensing, an additional source of independent long-term ex- trinsic variability, via a polynomial regression. Our Bayesian strategy adopts a Metropolis-Hastings within Gibbs sampler. We improve the sampler by using an ancillarity-sufficiency interweaving strategy and adaptive Markov chain Monte Carlo. We introduce a profile likeli- hood of the time delay as an approximation of its marginal posterior distribution. The Bayesian and profile likelihood approaches comple- ment each other, producing almost identical results; the Bayesian method is more principled but the profile likelihood is simpler to implement. We demonstrate our estimation strategy using simulated data of doubly- and quadruply-lensed quasars, and observed data from quasars Q0957+561 and J1029+2623 .
Issue Date: 5-Oct-2017
Date of Acceptance: 31-Jan-2017
URI: http://hdl.handle.net/10044/1/44294
DOI: https://dx.doi.org/10.1214/17-AOAS1027
ISSN: 1941-7330
Publisher: Institute of Mathematical Statistics (IMS)
Start Page: 1309
End Page: 1348
Journal / Book Title: Annals of Applied Statistics
Volume: 11
Issue: 3
Copyright Statement: © Institute of Mathematical Statistics, 2017
Sponsor/Funder: The Royal Society
Commission of the European Communities
National Science Foundation (US)
Funder's Grant Number: WM110023
FP7-PEOPLE-2012-CIG-321865
DMS 15-13484
Keywords: astro-ph.IM
astro-ph.CO
stat.AP
0104 Statistics
Statistics & Probability
Publication Status: Published
Appears in Collections:Mathematics
Statistics
Faculty of Natural Sciences



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