Cosmic shear measurement with maximum likelihood and maximum a posteriori inference

We investigate the problem of noise bias in maximum likelihoodand maximuma posteriori estimatorsfor 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 likelihoodinference for weak lensing. We show that a large part of the bias on these point estimatorscan 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 very promising results. We find that the introduction of an intrinsic shape prior mitigates noise bias, such that the maximuma posteriori estimatecan be made less biased than the maximum likelihoodestimate. 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. 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 estimatorsas tools for lensing inference, arguing that they allow for the robust measurement of ellipticity and shear.