Kavli Affiliate: Kaisey Mandel

| First 5 Authors: Hyungsuk Tak, Kaisey Mandel, David A. van Dyk, Vinay L. Kashyap, Xiao-Li Meng

| Summary:

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.

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