Taking the Weight Off: Mitigating Parameter Bias from Catastrophic Outliers in 3$\times$2pt Analysis

TL;DR

The paper addresses biases in 3$ imes$2pt cosmological inferences caused by catastrophic photo-$z$ outliers in Stage IV surveys. It models photo-$z$ uncertainties with mean shifts $\Delta z^i$ and an outlier fraction $f$ described by a Gaussian centered at $z=3.2$ with width $0.5$, and computes angular power spectra $C_\ell$ under the Limber approximation using $P_{mm}$ from 1-loop theory. Inference uses a Gaussian likelihood and affine-invariant MCMC, supplemented by PPCs to identify misspecifications, and introduces a composite likelihood with down-weighting factor $\gamma$ to mitigate biases. Across simulations, outliers can bias $\Omega_M$, $\sigma_8$ by up to $1.8\sigma$ and IA parameters by orders of magnitude, while the proposed reweighting reduces biases to $<1\sigma$ without substantially degrading constraints, providing a practical path for robust Stage IV analyses.

Abstract

Stage IV cosmological surveys will map the universe with unprecedented precision, reducing statistical uncertainties to levels where unmodelled systematics can significantly bias inference. In particular, photometric redshift (photo-z) errors and intrinsic alignments (IA) must be robustly accounted for to ensure accurate inference of cosmological parameters. The increasing depth of Stage IV surveys exacerbates these challenges by producing low signal-to-noise galaxy populations prone to inaccurate photo-z measurements. Catastrophically misidentified redshifts are especially problematic for 3$\times$2pt inferences that combine weak lensing and galaxy clustering information. We demonstrate that even modest outlier fractions (e.g. 5%) can lead to substantial biases in cosmological parameter estimates: up to 1.8$σ$ in $Ω_M$ and $σ_8$, and over 8$σ$ in the IA redshift evolution parameter $η$. To address this, we introduce a flexible weighting scheme at the likelihood level that down-weights the most contamination-sensitive elements of the data vector during inference. This method mitigates biases without inflating the parameter space, reducing cosmological parameter biases to below 1$σ$ without substantially degrading constraining power. Our approach offers a practical solution for future analyses, enabling robust cosmological inference in the presence of catastrophic redshift errors.

Figures (10)

• Figure 1: The cosmological inference process from a galaxy sample over redshift range $z$, to summary statistic $C_\ell$, to parameters of interest $\theta_i$.
• Figure 2: Redshift distributions for the five bins of the lens (left) and source (right) samples.
• Figure 3: The photo-$z$ distribution of source bin $\frac{dN_s^0}{dz}$ with mean shift $\Delta z^0 = 0.05$ and an outlier fraction of $f=0.1$. We use unrealistically large values here for clear visualisation. The fiducial source bins are plotted in grey for comparison.
• Figure 4: The posterior probability distributions for cosmological parameters $\Omega_M, \sigma_8$ (upper) and dark energy parameters (lower) for a subset of the scenarios described in Table \ref{['tab:scenarios']}. $\Delta \theta$ indicates the difference between the maximum a posteriori and the fiducial value (Table \ref{['tab:fiducial']}), where $\Delta \theta = 0$ is indicated with the dashed black line. Mean and 1$\sigma$ and 2$\sigma$ are indicated by the dark and light lines.
• Figure 5: The posterior predictive diagnostic plots for Scenario 5 for two weak lensing angular power spectra in the mock data. Catastrophic outliers included in the lowest bin affect cross-correlations significantly (left) while leaving the autocorrelation in higher bins unaffected (right). We plot the model as the mean of the 500 datavectors produced from sampling the posterior, with the shaded region indicating the 2$\sigma$ error, and plot the mock data as data points with 2$\sigma$ error bars drawn from the data covariance matrix.