Bayesian analysis of weak gravitational lensing

Abstract

This thesis is concerned with how to extract cosmological information from observations of weak gravitational lensing – the modification of observed galaxy images due to gravitational lensing by the large-scale structure of the Universe. Firstly, we are concerned with how we can use all possible observa- tional probes of weak lensing to squeeze out as much cosmological information as possible from future surveys. Up until now, the tra- ditional approach to cosmological weak lensing analyses have focused on the distortion of shapes of distant galaxies measured across the sky – cosmic shear. However, shearing of galaxy shapes is only half the picture – weak lensing also magnifies the sizes and fluxes of observed objects and this lensing magnification field contains the same cosmo- logical information as the cosmic shear field, whilst being subject to a different set of systematic effects. As such, weak lensing magnifica- tion is an exciting complement to cosmic shear and a holistic approach to weak lensing, combining shear and magnification, promises tighter constraints on cosmology, better control of systematics, and more ro- bust science at the end-of-the-day. We develop the theoretical and statistical formalism for performing a cosmological weak lensing anal- ysis using shape, size and flux information together and demonstrate that significant information gains and synergies can be expected from the addition of this new lensing observable – cosmic magnification. Secondly, we are interested in how we can use the statistics of the lensing fields to constrain cosmology via an analysis that is prin- cipled in its propagation of uncertainties, optimal in its use of the full information-content of the data, and exact under clearly stated and well understood model assumptions. We introduce a totally fresh perspective on weak lensing data analysis – Bayesian hierar- chical modelling (BHM) – that promises to achieve all of these goals. The BHM approach provides a general framework for analysing weak lensing data that accounts for the full statistical interdependency of all model components in the weak lensing analysis pipeline, allowing information to flow freely from (in principle) raw pixel and photo- metric data through to cosmological inferences. We develop efficient Bayesian sampling schemes that explore the joint posterior of the shear maps and power spectra (and cosmological parameters) from a catalogue of estimated shapes and redshifts. We demonstrate that these algorithms bring the benefits of the Bayesian approach whilst being computationally practical for current and future surveys, and are readily extendable to extract information beyond the two-point statistics of the lensing fields or to incorporate the full weak lensing pipeline in a global principled analysis, presenting significant advan- tages over traditional estimator-based methods. We apply the newly developed Bayesian hierarchical approaches to the current state-of- the-art cosmic shear data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), constraining cosmological parameters and models from weak lensing using Bayesian hierarchical inference – the first application to weak lensing data.