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Activity Number: 179
Type: Contributed
Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #316266 View Presentation
Title: Bayesian and Profile Likelihood Approaches to Time Delay Estimation for Stochastic Time Series of Gravitationally Lensed Quasars
Author(s): Hyungsuk Tak*
Companies: Harvard University
Keywords: Time delay ; Gravitational lensing ; Quasar ; State-space model ; Ornstein-Uhlenbeck process ; Ancilarity-sufficiency interweaving strategy
Abstract:

The gravitational field of a galaxy can act as a lens and deflect the light emitted by a more distant object. If the galaxy acts as a strong enough gravitational lens, it may cause multiple images of the same object to appear in the sky when viewed from Earth. Since the light in each gravitationally lensed image traverses a different path length, fluctuations in the source brightness are observed at different times in the several images. The time delay between these fluctuations in the time series of brightness data of each image can be used to constrain cosmological parameters, including the current expansion rate of the Universe. Our model is based on a state-space representation for an irregularly observed time series generated from a latent continuous-time Ornstein-Uhlenbeck process. Bayesian strategy adopts scientifically motivated hyper-prior distributions and a Gibbs sampler. A profile likelihood approach approximates the posterior distribution of the time delay. Both ways produce almost identical results, supplementing each other; the Bayesian way is more principled but the profile likelihood is simpler and faster. We illustrate our methods via simulated and observed data.


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