Title: TD-CARMA: Painless, accurate, and scalable estimates of gravitational-lens time delays with flexible CARMA processes
Authors: Antoine Meyer - Imperial College London (France) [presenting]
David van Dyk - Imperial College London (United Kingdom)
Aneta Siemiginowska - Harvard University (United States)
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. Cosmological parameters encoding our current understanding of the expansion history of the Universe can be constrained by accurate estimation of time delays. We propose TD-CARMA, a Bayesian method to estimate cosmological time delays by modelling the observed and irregularly sampled light curves as realizations of a CARMA process. Our model accounts for heteroskedastic measurement errors and microlensing, a source of independent extrinsic long-term variability. The CARMA formulation admits a linear state-space representation, allowing for efficient and scalable likelihood computation via the Kalman Filter. We obtain a sample from the joint posterior distribution using nested sampling. This allows for painless Bayesian Computation, dealing with the expected multi-modality of the posterior distribution in a straightforward manner and not requiring starting values for the time delay, unlike existing methods. In addition, the proposed sampling procedure automatically evaluates the Bayesian evidence, allowing us to perform principled Bayesian model selection. TD-CARMA is parsimonious, and typically includes no more than a dozen unknown parameters.