Cosmic shear measurement with maximum likelihood and maximum a posteriori inference

TL;DR

This paper develops bias correction methods for maximum likelihood and maximum a posteriori estimators in cosmic shear measurements, demonstrating their effectiveness on simulated data for future space surveys.

Contribution

It derives higher-order bias terms and shows how intrinsic shape priors can reduce noise bias in shear estimation, improving measurement accuracy.

Findings

Bias can be significantly reduced using likelihood information without external calibration.

Shape priors help mitigate noise bias, making MAP estimates less biased than ML estimates.

Bias propagation analysis suggests potential to meet space survey requirements.

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.