Building unbiased estimators from non-Gaussian likelihoods with application to shear estimation
- Physics and Astronomy Department, Stony Brook University, Stony Brook, NY 11794 (United States)
- Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA 94720 (United States)
- Brookhaven National Laboratory, Blgd 510, Upton NY 11375 (United States)
We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we expand the likelihood. We apply this formalism to rederive the optimal quadratic estimator and show how the replacement of the second derivative matrix with the Fisher matrix is a generic way of creating an unbiased estimator (assuming choice of the fiducial model is independent of data). Next we apply the approach to estimation of shear lensing, closely following the work of Bernstein and Armstrong (2014). Our first order estimator reduces to their estimator in the limit of zero shear, but it also naturally allows for the case of non-constant shear and the easy calculation of correlation functions or power spectra using standard methods. Both our first-order estimator and Bernstein and Armstrong's estimator exhibit a bias which is quadratic in true shear. Our third-order estimator is, at least in the realm of the toy problem of Bernstein and Armstrong, unbiased to 0.1% in relative shear errors Δg/g for shears up to |g|=0.2.
- OSTI ID:
- 22382026
- Journal Information:
- Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 01; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1475-7516
- Country of Publication:
- United States
- Language:
- English
An accurate and practical method for inference of weak gravitational lensing from galaxy images
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journal | April 2016 |
| An accurate and practical method for inference of weak gravitational lensing from galaxy images | text | January 2015 |
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