Propagating data-driven galaxy redshift distribution uncertainties in 3$\times$2-pt analyses

TL;DR

This paper evaluates different models for galaxy redshift distribution uncertainties in 3x2-pt analyses, recommending PCA models for their balance of accuracy and computational efficiency.

Contribution

It compares four uncertainty models, demonstrating PCA's effectiveness and proposing analytical marginalisation to incorporate complex models efficiently.

Findings

PCA models only slightly degrade constraints on S8.

Considering PCA reduces bias in parameters like Ωm and σ8.

Analytical marginalisation speeds up computations by up to 25 times.

Abstract

Uncertainties in the radial distribution of galaxies, $\boldsymbol{n}(\boldsymbol{z})$, are one of the major contributions to the error budget of early Stage-IV galaxy survey analyses of weak gravitational lensing, galaxy clustering and galaxy-galaxy lensing (3$\times$2-pt). Based on ensembles of simulated $\boldsymbol{n}(\boldsymbol{z})$ including stochastic and systematic variations, we study the impact of four different $\boldsymbol{n}(\boldsymbol{z})$ uncertainty models: shifts, shifts & stretches, Gaussian processes (GP) and principal component analysis (PCA). Due to the high dimensionality of the latter models, we make use of state-of-the-art gradient-based inference methods as well as approximate analytical marginalisation schemes. Our results show that Stage-IV 3$\times$2-pt analyses must go beyond simple shift & stretch models. In particular, we advocate for the adoption of PCA models even in early Stage-IV surveys. Our results show that considering a five-parameters PCA model only degrades the constraint on the $S_{\rm 8}$ parameter by $5$ per cent with respect to the case when only a shift and a stretch parameter are included, while incurring half the bias in its constituents parameters, $\Omega_{\rm m}$ and $\sigma_{\rm 8}$. We demonstrate that all models considered can be safely marginalised analytically, with speed-ups of up to a factor of 25 depending on the dimensionality of the model. This will allow Stage-IV analyses to safely include higher-dimensional $\boldsymbol{n}(\boldsymbol{z})$ uncertainty models in their analysis at negligible additional computational cost.