IOP : Beware of commonly used approximations : Part II. Estimating systematic biases in the best-fit parameters

Bernal, José Luis; Bellomo, Nicola; Raccanelli, Alvise; Verde, Licia

doi:10.1088/1475-7516/2020/10/017

Article
Report number	arXiv:2005.09666 ; CERN-TH-2020-054
Title	Beware of commonly used approximations : Part II. Estimating systematic biases in the best-fit parameters
Related title	Beware of commonly used approximations II: estimating systematic biases in the best-fit parameters
Author(s)	Bernal, José Luis ; Bellomo, Nicola ; Raccanelli, Alvise ; Verde, Licia
Publication	2020-10-06
Imprint	2020-05-19
Number of pages	21
Note	21 pages (+5 pages of appendices +6 pages of references), 8 figures, 1 table. Multi_CLASS can be found in https://github.com/nbellomo/Multi_CLASS
In:	JCAP 2010 (2020) 017
DOI	10.1088/1475-7516/2020/10/017 (publication)
Subject category	astro-ph.CO ; Astrophysics and Astronomy
Abstract	Cosmological parameter estimation from forthcoming experiments promise to reach much greater precision than current constraints. As statistical errors shrink, the required control over systematic errors increases. Therefore, models or approximations that were sufficiently accurate so far, may introduce significant systematic biases in the parameter best-fit values and jeopardize the robustness of cosmological analyses. We present a general expression to estimate a priori the systematic error introduced in parameter inference due to the use of insufficiently good approximations in the computation of the observable of interest or the assumption of an incorrect underlying model. Although this methodology can be applied to measurements of any scientific field, we illustrate its power by studying the effect of modeling the angular galaxy power spectrum incorrectly. We also introduce Multi_CLASS, a new, public modification of the Boltzmann code CLASS, which includes the possibility to compute angular cross-power spectra for two different tracers. We find that significant biases in most of the cosmological parameters are introduced if one assumes the Limber approximation or neglects lensing magnification in modern galaxy survey analyses, and the effect is in general larger for the multi-tracer case, especially for the parameter controlling primordial non-Gaussianity of the local type, $f_{\rm NL}$.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2020 IOP Publishing Ltd and Sissa Medialab

$Ratio of the estimated bias in the model parameters over the forecasted 68\% confidence level marginalized constraints for cases when the lensing magnification is included (blue) and not as a function of the assumed magnification bias parameter. We show results for uniform (green) and Euclid-like (red) galaxy redshift distributions, and with non-overlapping (top) and overlapping (bottom) redshift bins; note the change of scale in the $y$-axis between them. In all cases, the case for $\ell_{\rm max}(z)$ is shown with wide solid lines with circle markers, while thin solid lines without markers correspond to the case with constant $\ell_{\rm max}=200$. Dotted lines mark $\lvert\Delta_{{\rm syst},a}/\sigma_{\theta_a}\lvert=1$.$ $Ratio of the estimated bias in the model parameters over the forecasted 68\% confidence level marginalized constraints for cases when the lensing magnification is included (blue) and not as a function of the assumed magnification bias parameter. We show results for uniform (green) and Euclid-like (red) galaxy redshift distributions, and with non-overlapping (top) and overlapping (bottom) redshift bins; note the change of scale in the $y$-axis between them. In all cases, the case for $\ell_{\rm max}(z)$ is shown with wide solid lines with circle markers, while thin solid lines without markers correspond to the case with constant $\ell_{\rm max}=200$. Dotted lines mark $\lvert\Delta_{{\rm syst},a}/\sigma_{\theta_a}\lvert=1$.$ $Ratio of the estimated bias in the model parameters over the forecasted 68\% confidence level marginalized constraints for cases when the lensing magnification is included (blue) and not as a function of the assumed magnification bias parameter. We show results for uniform (green) and Euclid-like (red) galaxy redshift distributions, and with non-overlapping (top) and overlapping (bottom) redshift bins; note the change of scale in the $y$-axis between them. In all cases, the case for $\ell_{\rm max}(z)$ is shown with wide solid lines with circle markers, while thin solid lines without markers correspond to the case with constant $\ell_{\rm max}=200$. Dotted lines mark $\lvert\Delta_{{\rm syst},a}/\sigma_{\theta_a}\lvert=1$.$ Show more plots

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