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The skewed weak lensing likelihood: why biases arise, despite data and theory being sound
Sellentin, Elena; Heymans, Catherine; Harnois-Déraps, Joachim
AA(Département de Physique Théorique, Université de Genèe, 24 Quai Ernest-Ansermet, CH-1211 Genèe, Switzerland), AB(Scottish Universities Physics Alliance, Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK), AC(Scottish Universities Physics Alliance, Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK)
Monthly Notices of the Royal Astronomical Society, Volume 477, Issue 4, p.4879-4895 (MNRAS Homepage)
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methods: data analysis, methods: statistical, cosmology: observations
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2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society
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We derive the essentials of the skewed weak lensing likelihood via a simple hierarchical forward model. Our likelihood passes four objective and cosmology-independent tests which a standard Gaussian likelihood fails. We demonstrate that sound weak lensing data are naturally biased low, since they are drawn from a skewed distribution. This occurs already in the framework of Lambda cold dark matter. Mathematically, the biases arise because noisy two-point functions follow skewed distributions. This form of bias is already known from cosmic microwave background analyses, where the low multipoles have asymmetric error bars. Weak lensing is more strongly affected by this asymmetry as galaxies form a discrete set of shear tracer particles, in contrast to a smooth shear field. We demonstrate that the biases can be up to 30 per cent of the standard deviation per data point, dependent on the properties of the weak lensing survey and the employed filter function. Our likelihood provides a versatile framework with which to address this bias in future weak lensing analyses.
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