Cosmic shear measurement with maximum likelihood and maximum a posteriori inference

Abstract

We investigate the problem of noise bias in maximum likelihood and maximum a posteriori estimators for cosmic shear. We derive the leading and next-to-leading order biases and compute them in the context of galaxy ellipticity measurements, extending previous work on maximum likelihood inference for weak lensing. We show that a large part of the bias on these point estimators can be removed using information already contained in the likelihood when a galaxy model is specified, without the need for external calibration. We test these bias-corrected estimators on simulated galaxy images similar to those expected from planned space-based weak lensing surveys, with promising results. We find that the introduction of an intrinsic shape prior can help with mitigation of noise bias, such that the maximum a posteriori estimate can be made less biased than the maximum likelihood estimate. Second-order terms offer a check on the convergence of the estimators, but are largely sub-dominant. We show how biases propagate to shear estimates, demonstrating in our simple setup that shear biases can be reduced by orders of magnitude and potentially to within the requirements of planned space-based surveys at mild signal-to-noise. We find that second-order terms can exhibit significant cancellations at low signal-to-noise when Gaussian noise is assumed, which has implications for inferring the performance of shear-measurement algorithms from simplified simulations. We discuss the viability of our point estimators as tools for lensing inference, arguing that they allow for the robust measurement of ellipticity and shear.

20 pages, 16 figures. Added more low-S/N simulation results, broad conclusions unchanged. Matches version published in MNRAS

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Cited by in corpus (5)

• Effects of overlapping sources on cosmic shear estimation: Statistical sensitivity and pixel-noise bias
• Euclid preparation. LIII. LensMC, weak lensing cosmic shear measurement with forward modelling and Markov Chain Monte Carlo sampling
• Shear measurement bias I: dependencies on methods, simulation parameters and measured parameters
• Analytical Noise Bias Correction for Weak Lensing Shear Analysis with ERA
• Shear measurement bias II: a fast machine learning calibration method