Testing quadratic maximum likelihood estimators for forthcoming Stage-IV weak lensing surveys

Abstract

ABSTRACTHeadline constraints on cosmological parameters from current weak lensing surveys are derived from two-point statistics that are known to be statistically sub-optimal, even in the case of Gaussian fields. We study the performance of a new fast implementation of the Quadratic Maximum Likelihood (QML) estimator, optimal for Gaussian fields, to test the performance of Pseudo-Cℓ estimators for upcoming weak lensing surveys and quantify the gain from a more optimal method. Through the use of realistic survey geometries, noise levels, and power spectra, we find that there is a decrease in the errors in the statistics of the recovered E-mode spectra to the level of $\sim \!\! 20\, {{\ \rm per\ cent}}$ when using the optimal QML estimator over the Pseudo-Cℓ estimator on the largest angular scales, while we find significant decreases in the errors associated with the B-modes. This raises the prospects of being able to constrain new physics through the enhanced sensitivity of B-modes for forthcoming surveys that our implementation of the QML estimator provides. We test the QML method with a new implementation that uses conjugate-gradient and finite-differences differentiation methods resulting in the most efficient implementation of the full-sky QML estimator yet, allowing us to process maps at resolutions that are prohibitively expensive using existing codes. In addition, we investigate the effects of apodization, B-mode purification, and the use of non-Gaussian maps on the statistical properties of the estimators. Our QML implementation is publicly available and can be accessed from GitHub.