Testing Quadratic Maximum Likelihood estimators for forthcoming Stage-IV weak lensing surveys

Headline 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 ~20% 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 for the QML estimator. 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 apodisation, 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.

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