Blinding multi-probe cosmological experiments

TL;DR

This work addresses bias risks in multiprobe cosmology by introducing a summary-statistic blinding method that shifts input observables according to a reference cosmology plus a blind offset. The approach preserves internal consistency checks while concealing the true cosmological parameters, and is validated with DES Year 3–like simulations for the 3×2pt analysis. Results show small or negligible Δχ^2 under realistic shifts, supporting reliable unblinding once decisions are ready, and the method scales favorably with increasing measurement precision. The authors discuss practical considerations, potential caveats, and future extensions to broader observables and survey programs.

Abstract

The goal of blinding is to hide an experiment's critical results -- here the inferred cosmological parameters -- until all decisions affecting its analysis have been finalised. This is especially important in the current era of precision cosmology, when the results of any new experiment are closely scrutinised for consistency or tension with previous results. In analyses that combine multiple observational probes, like the combination of galaxy clustering and weak lensing in the Dark Energy Survey (DES), it is challenging to blind the results while retaining the ability to check for (in)consistency between different parts of the data. We propose a simple new blinding transformation that works by modifying the summary statistics that are input to parameter estimation, such as two-point correlation functions. The transformation shifts the measured statistics to new values that are consistent with (blindly) shifted cosmological parameters, while preserving internal (in)consistency. We apply the blinding transformation to simulated data for the projected DES Year 3 galaxy clustering and weak lensing analysis, demonstrating that practical blinding is achieved without significant perturbation of internal-consistency checks, as measured here by degradation of the $χ^2$ between data and best-fitting model. Our blinding method conserves $χ^2$ more precisely as experiments evolve to higher precision.

Figures (13)

• Figure 1: Cartoon of model and data spaces that we consider when thinking about how to blind an analysis, as discussed in Sect. \ref{['sec:shiftenough']}. ${\cal M}$ is the space of all viable model parameter sets $\Theta$, which projects onto the observable-vector space ${\cal D}_{\operatorname{\pi}\xspace}\xspace\subset{\cal D}\xspace$, where ${\cal D}$ is the space of all possible observable vectors. ${\cal M}_{\operatorname{Prej}\xspace}$ is a region in parameter space associated with what we refer to as the "prejudice" distribution, describing experimenters' preconceived expectations for where $\Theta$ is likely to be. This subset of parameter space projects onto ${\cal D}_{\operatorname{Prej}\xspace}\xspace\subset{\cal D}_{\operatorname{\pi}\xspace}\xspace$. An effective blinding transformation must have the possibility of moving the observable vector $\hat{{\mathbf{d}}}$ in or out of ${\cal D}_{\operatorname{Prej}\xspace}$ without moving it out of the prior space ${\cal D}_{\operatorname{\pi}\xspace}$.
• Figure 2: The $n(z)$ redshift distributions for lens and source galaxies in the DES Y1-3$\times$2pt analysis from Abbott:2017wau. The vertical coloured bands show the nominal redshift range of each bin, while the lines show the estimated true redshift distribution when galaxies are binned in photometric redshift. The black lines show the unbinned total distribution. We adopt these same redshift distributions for our Y3 blinding tests.
• Figure 3: Values (off-diagonal panels) and the distribution (diagonal panels) of parameters $\sigma_8$, $w$, and $\Omega_m$ in the 100 realizations used for the fiducial test of our blinding procedure. The blue circles are the observed (that is true, unblinded) parameter values. The red circles are the shifted values used to blind the data. The dashed lines denote the reference model used for blinding.
• Figure 4: The 68 and 95% confidence intervals for blinded (green) and unblinded (blue) synthetic DES Y3-3$\times$2pt data. As an illustrative example, results are shown for a realization of the fiducial blinding test with a large input blinding shift of $(\Delta\sigma_8 =-0.117,\Delta w=+0.314)$ and a low $\Delta\chi^2\xspace=1.86$. Dashed gray lines show the input parameters used to simulate the unblinded data $\Theta_{\rm obs}\xspace=(\sigma_8=0.826$, $w=-0.912$, $\Omega_m-0.29$). The black, thick arrow shows the points from $\Theta_{\rm ref}$ to $\Theta_{\rm ref}\xspace+\Delta\Theta\xspace$ to show the input blinding shift, and the red, thin arrow points from $\Theta_{\rm unbl}\xspace=\Theta_{\rm obs}\xspace$ to $\Theta_{\rm bl}\xspace$ to show the change in best-fitting parameters.
• Figure 5: Fiducial blinding test results for $\Delta\chi^2$. The top axis shows $\Delta\chi^2$ in units of the degrees of freedom associated with the DES Y3-3$\times$2pt $w$CDM analysis, $\nu=430$.