Pith. sign in

REVIEW 2 major objections 2 minor 2 references

Stage-IV 3x2-pt analyses must adopt PCA models for n(z) uncertainties rather than simple shift and stretch parameters.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.3

2026-07-04 01:45 UTC pith:CEMZROXY

load-bearing objection The paper's core result is that a 5-param PCA n(z) model costs only 5% on S8 precision versus shift+stretch but halves bias on Omega_m/sigma_8, with analytical marginalization delivering up to 25x speed-up. the 2 major comments →

arxiv 2604.24425 v2 pith:CEMZROXY submitted 2026-04-27 astro-ph.CO

Propagating data-driven galaxy redshift distribution uncertainties in 3times2-pt analyses

Jaime Ruiz-Zapatero , Qianjun Hang , Yun-Hao Zhang , Benjamin Joachimi , Joe Zuntz , Ian Harrison , Carlos Garc\'ia-Garc\'ia , Alex Malz
show 2 more authors
Benjamin St\"olzner the LSST Dark Energy Science Collaboration
This is my paper
classification astro-ph.CO
keywords galaxy redshift distributions3x2-pt analysesweak gravitational lensinggalaxy clusteringn(z) uncertaintiesprincipal component analysisStage-IV surveysanalytical marginalisation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper compares four models for propagating uncertainties in galaxy redshift distributions n(z) through combined weak lensing, clustering, and galaxy-galaxy lensing measurements. Using ensembles of simulated n(z) that incorporate both stochastic and systematic variations, it tests shifts, shifts plus stretches, Gaussian processes, and principal component analysis. The central finding is that even early Stage-IV surveys need the higher-dimensional PCA approach. A five-parameter PCA model worsens the constraint on S8 by only five percent compared with the simpler shift-and-stretch case, yet it halves the bias that appears in the separate parameters Omega_m and sigma_8. All four models can be marginalised analytically, yielding speed-ups of up to a factor of twenty-five.

Core claim

Considering a five-parameters PCA model only degrades the constraint on the S8 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_m and sigma_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. Stage-IV 3x2-pt analyses must go beyond simple shift and stretch models.

What carries the argument

Principal component analysis models of n(z) uncertainties, constructed from ensembles of simulated redshift distributions that encode stochastic and systematic variations, with analytical marginalisation applied to the resulting high-dimensional parameter spaces.

Load-bearing premise

The ensembles of simulated n(z) that include stochastic and systematic variations are representative of the actual uncertainties present in real Stage-IV survey data.

What would settle it

Application of the same five-parameter PCA versus shift-and-stretch comparison to actual Stage-IV survey data that produces a degradation in the S8 constraint larger than five percent or a bias reduction smaller than a factor of two.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Stage-IV 3x2-pt analyses must go beyond simple shift and stretch models for n(z) uncertainties.
  • A five-parameter PCA model degrades the S8 constraint by only 5 percent relative to shift-and-stretch but halves the bias in Omega_m and sigma_8.
  • All four n(z) uncertainty models can be marginalised analytically with computational speed-ups reaching a factor of 25.
  • PCA models can be adopted even in early Stage-IV surveys at negligible extra cost.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The analytical marginalisation technique could be combined with existing gradient-based samplers to handle still-higher-dimensional n(z) models without prohibitive runtime.
  • The same simulated-ensemble approach might be used to propagate n(z) uncertainties into other large-scale-structure statistics beyond the 3x2-pt combination.
  • If real survey data confirm the simulated ensembles, the 5-percent degradation figure provides a concrete budget item for survey design decisions on redshift calibration.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a study on propagating uncertainties in galaxy redshift distributions n(z) for 3×2-pt cosmological analyses in Stage-IV surveys. Based on simulated ensembles of n(z) that incorporate stochastic and systematic variations, the authors compare four uncertainty models: shifts, shifts and stretches, Gaussian processes, and principal component analysis (PCA). They conclude that analyses must go beyond simple shift and stretch models and advocate for PCA models, showing that a five-parameter PCA model degrades the S8 constraint by only 5% compared to shift and stretch while halving the bias on Ωm and σ8. Additionally, they demonstrate that all models can be analytically marginalized with computational speed-ups of up to a factor of 25.

Significance. If the simulated n(z) ensembles are representative of real survey uncertainties, this work is significant for guiding the modeling choices in early Stage-IV analyses. It provides quantitative evidence that higher-dimensional PCA models are viable with only modest degradation in parameter constraints and better bias control. The demonstration of safe analytical marginalization for high-dimensional models is a practical strength, as it enables efficient computation without sacrificing accuracy. This could influence analysis pipelines for surveys like LSST and Euclid by encouraging more sophisticated n(z) uncertainty treatments at negligible extra cost.

major comments (2)
  1. [Methods section on n(z) ensemble construction] The central claims regarding the 5% degradation in S8 constraints and halved bias on Ωm and σ8 (as stated in the abstract) depend on the simulated ensembles accurately representing the uncertainties in real Stage-IV photo-z pipelines. The paper should include explicit tests or comparisons showing that the included stochastic and systematic variations capture key effects such as calibration residuals, inter-bin correlations, or non-Gaussian features present in actual data from LSST or Euclid. Without this, the relative performance metrics and recommendation for PCA models may not generalize beyond the specific simulation setup.
  2. [Results section on analytical marginalization] The abstract states that all models can be safely marginalised analytically with speed-ups up to a factor of 25. For the 5-parameter PCA case, which is load-bearing for the advocacy of PCA, please specify the section presenting the explicit comparison between analytical and full numerical marginalization results, including any quantified residual biases or coverage tests.
minor comments (2)
  1. [Abstract] The abstract mentions 'state-of-the-art gradient-based inference methods' but does not name them (e.g., NUTS or variational inference); adding this detail would improve clarity for readers.
  2. [Throughout manuscript] Notation for the redshift distribution should be checked for consistency (bold vector vs. non-bold) across text, equations, and figure captions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address each major comment below, providing clarifications on the scope of our simulation study and pointing to the relevant sections for the marginalization results. We will incorporate revisions to improve clarity without altering the core findings.

read point-by-point responses

  1. Referee: [Methods section on n(z) ensemble construction] The central claims regarding the 5% degradation in S8 constraints and halved bias on Ωm and σ8 (as stated in the abstract) depend on the simulated ensembles accurately representing the uncertainties in real Stage-IV photo-z pipelines. The paper should include explicit tests or comparisons showing that the included stochastic and systematic variations capture key effects such as calibration residuals, inter-bin correlations, or non-Gaussian features present in actual data from LSST or Euclid. Without this, the relative performance metrics and recommendation for PCA models may not generalize beyond the specific simulation setup.

    Authors: Our study is explicitly a controlled simulation analysis using ensembles that incorporate stochastic and systematic variations motivated by known photo-z effects (as detailed in the Methods section). We do not claim direct equivalence to real LSST/Euclid data and will add a clarifying paragraph in the Discussion section on the assumptions and limitations of generalization. This addresses the concern without requiring new tests against proprietary real data, which is outside the paper's scope. The relative performance metrics remain valid within the simulated framework. revision: partial

  2. Referee: [Results section on analytical marginalization] The abstract states that all models can be safely marginalised analytically with speed-ups up to a factor of 25. For the 5-parameter PCA case, which is load-bearing for the advocacy of PCA, please specify the section presenting the explicit comparison between analytical and full numerical marginalization results, including any quantified residual biases or coverage tests.

    Authors: The explicit comparison between analytical and numerical marginalization for the 5-parameter PCA model, including quantified residual biases and coverage tests, is presented in Section 4.3 (Results on analytical marginalization). We will revise the abstract to include a direct reference to this section for improved clarity. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's central results on model performance (5% S8 degradation and halved bias for 5-param PCA vs shift+stretch) are obtained by propagating four n(z) uncertainty models through forward-simulated ensembles and standard 3x2-pt cosmological likelihoods, followed by gradient-based sampling or analytical marginalization. These metrics are computed outputs of the simulation pipeline rather than quantities defined in terms of the fitted parameters themselves or reduced by construction. No self-citation load-bearing steps, uniqueness theorems, or ansatzes imported from prior author work appear in the load-bearing claims; the analytical marginalization is a standard computational technique applied uniformly. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on the assumption that the simulated n(z) ensembles capture the relevant uncertainties and that standard 3x2-pt likelihoods plus gradient-based samplers are sufficient to propagate them; no new physical entities are introduced.

free parameters (2)
  • shift and stretch parameters
    Two parameters used in the baseline n(z) uncertainty model; their values are varied across the simulated ensembles.
  • PCA component amplitudes (5 parameters)
    Coefficients of the five principal components retained in the higher-dimensional n(z) uncertainty model.
axioms (2)
  • domain assumption Simulated ensembles of n(z) with stochastic and systematic variations are representative of real survey uncertainties.
    Invoked in the first sentence of the abstract as the basis for studying model impact.
  • domain assumption Standard 3x2-pt likelihoods and cosmological parameter inference pipelines remain valid when n(z) uncertainties are included via the tested models.
    Implicit in the comparison of constraints on S8, Omega_m and sigma_8.

pith-pipeline@v0.9.1-grok · 5865 in / 1516 out tokens · 29416 ms · 2026-07-04T01:45:57.324705+00:00 · methodology

0 comments
read the original 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.

Figures

Figures reproduced from arXiv: 2604.24425 by Alex Malz, Benjamin Joachimi, Benjamin St\"olzner, Carlos Garc\'ia-Garc\'ia, Ian Harrison, Jaime Ruiz-Zapatero, Joe Zuntz, Qianjun Hang, The LSST Dark Energy Science Collaboration, Yun-Hao Zhang.

Figure 1
Figure 1. Figure 1: The ensembles of redshift galaxy distributions from the CosmoDC2 catalogue produced by Zhang et al. (2026) for each tomographic bin for the lens (top row) and source samples (bottom row). Each ensemble contains the statistical uncertainties of the CosmoDC2 catalogue as given by the FlexZBoost algorithm as well as systematic uncertainties due to the incompleteness of the reference sample. spectra between th… view at source ↗
Figure 2
Figure 2. Figure 2: A comparison between the measured galaxy redshift distribution, 𝒏(𝒛), for the first tomographic bin of the lens sample by Zhang et al. (2026) and the 𝒏(𝒛) samples generated by different uncertainty models (shifts, shifts & stretches, PCAs and GPs) after being calibrated on the former. The upper panels show overlapping samples of the processes. The lower panels show the correlation matrices of the processes… view at source ↗
Figure 3
Figure 3. Figure 3: The posteriors for the galaxy distribution of each tomographic bin given by different uncertainty models. Upper panels show the lens sample bins. Lower panels show the source sample bins. The first row of panels in each block shows a direct comparison between the galaxy distributions obtained for each model. In the rows below we show the standard deviation on the 𝒏(𝒛) posterior obtained by every model cons… view at source ↗
Figure 5
Figure 5. Figure 5: The 1 & 2D marginalised constraints for the cosmological pa￾rameters 𝑆8 and ⟨𝑏𝑔 ⟩, the average galaxy bias across all tomographic bins, accounting for galaxy distribution uncertainties using different models. Black dashed contours correspond to when no model was considered (i.e. galaxy distribution uncertainties were not considered in the analysis). Blue contours correspond to the shifts (Δz) model posteri… view at source ↗
Figure 6
Figure 6. Figure 6: The standard deviation of the galaxy bias parameter of each to￾mographic bin in the lens sample. The labels on the horizontal axis corre￾spond to the mean redshift of each tomographic bin. The different error bars represent the constraints from the different galaxy distribution uncertainty models considered in this work. Black lines correspond to when no model was considered (i.e. galaxy distribution uncer… view at source ↗
Figure 7
Figure 7. Figure 7: Reduced 𝜒 2 distributions obtained when assuming a given galaxy distribution uncertainty model to fit noiseless data vectors based on the sam￾ples in the 𝒏(𝒛) calibration ensemble for shared cosmology. Thus the 𝜒 2 distributions shown represent the error incurred by assuming a given model. Models with a higher error will lead to a higher bias in the cosmology param￾eters. The black dashed line corresponds … view at source ↗
Figure 8
Figure 8. Figure 8: Square root bias over standard deviation as a percentage induced on the cosmological parameters Ωm (bottom panel) and 𝜎8 (top panel) purely due to the choice of 𝒏(𝒛) uncertainty model. The bias measurement was obtained using a linear approximation to fit theory vectors generated using 𝒏(𝒛) samples from the calibration ensemble using theory vectors generated based on the 𝒏(𝒛) given by each model. The standa… view at source ↗
Figure 9
Figure 9. Figure 9: The 1 & 2D marginalised constraints for the cosmological parameters Ωm, 𝜎8 and 𝑆8, accounting for 𝒏(𝒛) uncertainties using different models and different marginalisations techniques. In each sub-panel three different contours are compared. First, a set of black dashed contours show the constraints obtained when the parameters of the associated model were kept fixed. Second, the two sets of coloured contour… view at source ↗
Figure 10
Figure 10. Figure 10: A comparison between the 1D marginal 𝑆8 distributions obtained when considering different galaxy redshift distribution uncertainty models with respect the case where no model is considered. We show constraints for when a shift model (blue), a shift & stretch model (yellow), a PCA model (green) and a GP model (orange). Full opacity bars correspond to numerical constraints while half opacity bars correspond… view at source ↗

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages · 2 internal anchors

  1. [1]

    Dimensional reduction for sampled priors and application to photometric redshift distributions

    Astropy Collaboration et al., 2013, A&A, 558, A33 Astropy Collaboration et al., 2018, aj, 156, 123 Baum W. A., 1957, AJ, 62, 6 Benítez N., 2000, ApJ, 536, 571 Bernstein G., et al., 2025, arXiv e-prints, p. arXiv:2506.00758 Betancourt M., 2017, arXiv e-prints, p. arXiv:1701.02434 Bridle S., King L., 2007, New Journal of Physics, 9, 444 Campagne J.-E., et a...

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/b98835 2013

  2. [2]

    Forward-Mode Automatic Differentiation in Julia

    Cambridge, MA 02142 Rau M. M., et al., 2023, MNRAS, 524, 5109 Revels J., Lubin M., Papamarkou T., 2016, arXiv:1607.07892 [cs.MS] Robnik J., Seljak U., 2023, arXiv e-prints, p. arXiv:2303.18221 Robnik J., De Luca G. B., Silverstein E., Seljak U., 2022, arXiv e-prints, p. arXiv:2212.08549 Ruiz-Zapatero J., Hadzhiyska B., Alonso D., Ferreira P. G., García-Ga...

    work page internal anchor Pith review Pith/arXiv arXiv 2023