2016/09/30 by P. Šimon, Patrick Simon, Peter Schneider · 15 citations
Mathematics · Physics and Astronomy · #Adaptive optics and wavefront sensing #Artificial intelligence #Astrophysics #Brightness #Classical mechanics #Computer science #Estimator #Galaxies: Formation, Evolution, Phenomena #Galaxy #Gamma-ray bursts and supernovae #Gravitational lens #Image (mathematics) #Mathematics #Moment (physics) #Noise (video) #Optics #Physics #Statistical physics #Statistics #Weak gravitational lensing #astro-ph.CO
paper · pdf · doi:10.1051/0004-6361/201629591
published in Astronomy and Astrophysics 604, A109 (EDP Sciences) · 18 pages; 5 figures; accepted by A&A after major revision, especially of Sect. 3.3 that corrects the previous discussion on the bias by marginalization
arxiv created 2017/05/18 · openalex publication_date 2017/05/26 · arxiv updated 2017/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In weak gravitational lensing, weighted quadrupole moments of the brightness profile in galaxy images are a common way to estimate gravitational shear. We have employed general adaptive moments (GLAM ) to study causes of shear bias on a fundamental level and for a practical definition of an image ellipticity. The GLAM ellipticity has useful properties for any chosen weight profile: the weighted ellipticity is identical to that of isophotes of elliptical images, and in absence of noise and pixellation it is always an unbiased estimator of reduced shear. We show that moment-based techniques, adaptive or unweighted, are similar to a model-based approach in the sense that they can be seen as imperfect fit of an elliptical profile to the image. Due to residuals in the fit, moment-based estimates of ellipticities are prone to underfitting bias when inferred from observed images. The estimation is fundamentally limited mainly by pixellation which destroys information on the original, pre-seeing image. We give an optimised estimator for the pre-seeing GLAM ellipticity and quantify its bias for noise-free images. To deal with images where pixel noise is prominent, we consider a Bayesian approach to infer GLAM ellipticity where, similar to the noise-free case, the ellipticity posterior can be inconsistent with the true ellipticity if we do not properly account for our ignorance about fit residuals. This underfitting bias, quantified in the paper, does not vary with the overall noise level but changes with the pre-seeing brightness profile and the correlation or heterogeneity of pixel noise over the image. Furthermore, when inferring a constant ellipticity or, more relevantly, constant shear from a source sample with a distribution of intrinsic properties (sizes, centroid positions, intrinsic shapes), an additional, now noise-dependent bias arises towards low signal-to-noise if incorrect prior densities for the intrinsic properties are used. We discuss the origin of this prior bias. With regard to a fully-Bayesian lensing analysis, we point out that passing tests with source samples subject to constant shear may not be sufficient for an analysis of sources with varying shear.