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

Hyungsuk Tak, Kaisey Mandel, David A. Van Dyk, Vinay L. Kashyap, Xiao Li Meng, Aneta Siemiginowska

Research output: Contribution to journalArticle

7 Citations (Scopus)

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 appear in the sky. Since the light in each gravitationally lensed image traverses a different path length from the quasar to the Earth, fluctuations 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 extrinsic 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 likelihood of the time delay as an approximation of its marginal posterior distribution. The Bayesian and profile likelihood approaches complement 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.

Original languageEnglish (US)
Pages (from-to)1309-1348
Number of pages40
JournalAnnals of Applied Statistics
Volume11
Issue number3
DOIs
StatePublished - Sep 2017

Fingerprint

Quasars
Time Delay
Time delay
Profile Likelihood
Curve
Time series
Luminance
Estimate
Brightness
Galaxies
Markov processes
Ancillarity
Lenses
Fluctuations
Metropolis-Hastings
Gravitational Lensing
State-space Representation
Earth (planet)
Polynomial Regression
Polynomials

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty

Cite this

Tak, Hyungsuk ; Mandel, Kaisey ; Van Dyk, David A. ; Kashyap, Vinay L. ; Meng, Xiao Li ; Siemiginowska, Aneta. / Bayesian estimates of astronomical time delays between gravitationally lensed stochastic light curves. In: Annals of Applied Statistics. 2017 ; Vol. 11, No. 3. pp. 1309-1348.
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Bayesian estimates of astronomical time delays between gravitationally lensed stochastic light curves. / Tak, Hyungsuk; Mandel, Kaisey; Van Dyk, David A.; Kashyap, Vinay L.; Meng, Xiao Li; Siemiginowska, Aneta.

In: Annals of Applied Statistics, Vol. 11, No. 3, 09.2017, p. 1309-1348.

Research output: Contribution to journalArticle

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