A Systematic Study of Projection Biases in Weak Lensing Analysis

TL;DR

This paper systematically investigates how projection biases affect weak lensing analysis in DES, revealing their dependence on parameter priors and true values, and quantifying their impact on credible intervals and coverage.

Contribution

It provides a comprehensive analysis of projection biases in weak lensing, highlighting their dependence on parameter priors and true values, and estimates their effects on future DES data analyses.

Findings

Projection biases can exceed 1.5σ when true parameters are near prior bounds.

1D credible intervals can be overestimated by up to 30%.

Coverage can be as low as 27% due to biases.

Abstract

We present a systematic study of projection biases in the weak lensing analysis of the first year of data from the Dark Energy Survey (DES) experiment. In the analysis we used a $\Lambda$CDM model and three two-point correlation functions. We show that these biases are a consequence of projecting, or marginalizing, over parameters like $h$, $\Omega_b$, $n_s$ and $\Omega_\nu h^2$ that are both poorly constrained and correlated with the parameters of interest like $\Omega_m$, $\sigma_8$ and $S_8$. Covering the relevant parameter space we show that the projection biases are a function of where the true values of the poorly constrained parameters lie with respect to the parameter priors. For example, biases in the position of the posteriors can exceed the 1.5$\sigma$ level if the true values of $h$ and $n_s$ are close to the top of the prior's range and the true values of $\Omega_b$ and $\Omega_\nu h^2$ are close to the bottom of the range of their priors. We also show that in some cases the 1D credible intervals can be over-specified by as much as 30% and coverage can be as low as 27%. Finally we estimate these projection biases for the analysis of three and six years worth of DES data.