We provide a toolbox to estimate the time delay between the brightness time series of gravitationally lensed quasar images via Bayesian and profile likelihood approaches. The model is based on a state-space representation for irregularly observed time series data generated from a latent continuous-time Ornstein-Uhlenbeck process. Our Bayesian method adopts scientifically motivated hyper-prior distributions and a Metropolis-Hastings within Gibbs sampler, producing posterior samples of the model parameters that include the time delay. A profile likelihood of the time delay is a simple approximation to the marginal posterior distribution of the time delay. Both Bayesian and profile likelihood approaches complement each other, producing almost identical results; the Bayesian way is more principled but the profile likelihood is easier to implement.
|Author||Hyungsuk Tak, Kaisey Mandel, David A. van Dyk, Vinay L. Kashyap, Xiao-Li Meng, and Aneta Siemiginowska|
|Date of publication||2016-12-13 07:57:22|
|Maintainer||Hyungsuk Tak <firstname.lastname@example.org>|
bayesian: Estimating the time delay via the Bayesian method
entirelogprofilelikelihood: Calculating the entire profilel likelihood curve over the...
simple: Simulated simple data of a doubly-lensed quasar
timedelay-internal: Internal 'bayesian' functions
timedelay-package: Time Delay Estimation for Stochastic Time Series of...