Machine learning methods for delay estimation in gravitationally lensed signals

[摘要] Strongly lensed variable quasars can serve as precise cosmological probes, provided that time delays between the image fluxes can be accurately measured. This thesis, explores in detail a new approach based on kernel regression estimates, which is able to estimate a single time delay given several data sets for the same quasar. We develop realistic artificial data sets in order to carry out controlled experiments to test the performance of this new approach. We also test our method on real data from strongly lensed quasar Q0957+561 and compare our estimates against existing results. Furthermore, we attempt to resolve the problem for smaller delays in gravitationally lensed photon streams. We test whether a more principled treatment of delay estimation in lensed photon streams, compared with the standard kernel estimation method, can have benefits of more accurate (less biased) and/or more stable (less variance) estimation. To that end, we propose a delay estimation method in which a single latent nonhomogeneous Poisson process underlying the lensed photon streams is imposed. The rate function model is formulated as a linear combination of nonlinear basis functions. Such a unifying rate function is then used in delay estimation based on the corresponding Innovation Process.

[发布机构] University:University of Birmingham;Department:School of Computer Science

[关键词] Q Science;QA Mathematics;QA75 Electronic computers. Computer science