On the Probability Distributions of Ellipticity
Massimo Viola, Thomas Kitching, Benjamin Joachimi

TL;DR
This paper derives an exact 2D probability distribution for ellipticity measurements under Gaussian noise, highlighting biases in estimators and implications for weak lensing survey calibration.
Contribution
It generalizes the known ratio distribution to the multivariate case for ellipticity, providing a new analytical tool for weak lensing data analysis.
Findings
Bias in maximum likelihood ellipticity estimates identified.
Calibration strategies for upcoming surveys quantified.
Stokes parameters offer unbiased shear estimates with high variance.
Abstract
In this paper we derive an exact full expression for the 2D probability distribution of the ellipticity of an object measured from data, only assuming Gaussian noise in pixel values. This is a generalisation of the probability distribution for the ratio of single random variables, that is well-known, to the multivariate case. This expression is derived within the context of the measurement of weak gravitational lensing from noisy galaxy images. We find that the third flattening, or epsilon-ellipticity, has a biased maximum likelihood but an unbiased mean; and that the third eccentricity, or normalised polarisation chi, has both a biased maximum likelihood and a biased mean. The very fact that the bias in the ellipticity is itself a function of the ellipticity requires an accurate knowledge of the intrinsic ellipticity distribution of the galaxies in order to properly calibrate shear…
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Taxonomy
TopicsReservoir Engineering and Simulation Methods · Adaptive optics and wavefront sensing · Statistical and numerical algorithms
