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Forecasting the Impact of Source Galaxy Photometric Redshift Uncertainties on the LSST $3\times2$pt Analysis

T0 review · 2 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Marginalizing over a 15-parameter photo-z model inflates LSST Y10 3x2pt contours by 3.4x in ($\Omega_m$, $\sigma_8$) and 3.2x in ($w_0$, $w_a$), and cosmic-shear contours by 3.8x and 6.3x, versus fixing the redshift model.

desk verdict Solid, useful Fisher forecast with a realistic photo-z model, worth citing, but the headline cosmic-shear contour factors are prior-sensitive and the paper's claim that prior width doesn't matter is contradicted by its own Table C1. read the letter →

arxiv 2507.01374 v1 pith:CUOVTP6I submitted 2025-07-02 astro-ph.CO

Tianqing Zhang , Husni Almoubayyed , Rachel Mandelbaum , Markus Michael Rau , Nikolina Šarčević , C. Danielle Leonard , Jeffrey A. Newman , Brett Andrews
show 2 more authors
Shuang Liang The LSST Dark Energy Science Collaboration
This is my paper
classification astro-ph.CO PACS 98.80.Es95.36.+x
keywords photometricredshifts3x2ptanalysiscosmicshearFisherforecastingLSSTY10redshiftdistributioncalibrationintrinsicalignmentssourceoutliers
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Photometric redshifts (photo-z) are the inferred distances of the source galaxies whose shapes LSST will measure, and the paper's aim is to show that their uncertainties are a leading, quantifiable cost to the Year-10 3x2pt and cosmic shear analyses. The authors build a Fisher forecast code, FisherA2Z, that describes each of five source redshift bins with three nuisance parameters — a redshift bias, a width, and an outlier fraction — giving 15 photo-z parameters alongside cosmological, galaxy-bias, and intrinsic-alignment parameters. The central numerical result is that marginalizing over those 15 parameters enlarges the 2-$\sigma$ ($\Omega_m$, $\sigma_8$) contour by a factor of 3.4 for 3x2pt and 3.8 for cosmic shear, and the dark-energy ($w_0$, $w_a$) contour by 3.2 and 6.3, relative to fixing the redshift model; cosmic shear alone therefore becomes photo-z-limited, while the 3x2pt combination partially self-calibrates the errors. A decision-tree analysis then shows which photo-z parameters matter most, finding that $S_8$ responds most strongly to the mean redshift of the fourth source bin in the 3x2pt analysis. A sympathetic reader should care because these numbers convert a general worry about redshift calibration into concrete priorities for spectroscopic training surveys.

What carries the argument

The load-bearing object is the redshift distribution model of Eq. (3): each of the five source bins is a Gaussian core whose mean is shifted by a bias $\delta z_i$ and whose width is set by $\sigma_i$, both scaled by $(1+z_{\mathrm{center},i})$, plus an empirically fixed outlier population $n_{\mathrm{out}}(z)$ weighted by a per-bin outlier fraction $f_{\mathrm{out},i}$ — fifteen nuisance parameters in total. Around that model sits the 36-parameter Fisher information matrix computed by FisherA2Z, the likelihood-curvature estimate of parameter uncertainty, built with numerical derivatives, Gaussian priors, and a covariance matrix taken from the survey's science requirements forecast. Two further pieces of machinery carry the argument: the first-order bias formula of Eq. (13), which converts a wrong photo-z model into shifts in cosmological parameters, and a decision-tree feature-importance analysis (Gini importance over 5000 sampled redshift parameter sets) that ranks which of the fifteen parameters most drives the bias in each cosmological parameter.

What would settle it

Recompute the Fisher forecast with a covariance matrix generated for FisherA2Z's own data vector and check the four headline ratios (3.4 and 3.2 for 3x2pt; 3.8 and 6.3 for cosmic shear): if any changes by more than a few percent, the headline inflation factors are artifacts of the borrowed covariance. As a second check, run a full MCMC posterior for the same 36-parameter model and covariance, since the paper itself warns that its first-order bias formula overestimates cosmological bias; the contour-inflation factors should survive the MCMC while the 2-3.4 sigma bias predictions may shrink.

Watch

Extended reading notes

Core claim

Stated on the paper's own terms, the claim is that a realistic 15-parameter model of source photo-z errors changes the expected performance of LSST Y10: after marginalizing the redshift distribution, the 2-$\sigma$ ($\Omega_m$, $\sigma_8$) contour areas grow by factors of 3.4 (3x2pt) and 3.8 (cosmic shear), and the ($w_0$, $w_a$) contour areas by 3.2 and 6.3, so the cosmic-shear analysis is redshift-uncertainty-limited without external calibration. The same 36-parameter Fisher machinery, with data vectors from the Core Cosmology Library and a covariance matrix inherited from the DESC-SRD forecast, predicts that adopting externally calibrated photo-z error values in place of the fiducial ones would bias $\Omega_m$, $w_0$, and $w_a$ by roughly 2 $\sigma$ and $\sigma_8$ by 3.4 $\sigma$. The analysis also finds that the three probes are far from interchangeable: single-probe contours are 6-34 times larger than the 3x2pt contours, and the feature-importance study attributes the largest influence on $S_8$ to the mean redshift of the fourth source bin, while bin 2's bias and variance dominate $\Omega_m$, $\sigma_8$, and $w_0$. Finally, the training-set forecasts show the figure of merit rising with the number of spectroscopic galaxies and with the representativeness of galaxies above $z = 1.6$, with the full bias-variance-outlier model preferred by Bayes factors only when that representativeness exceeds about 0.5 for cosmic shear and 0.7 for 3x2pt.

Load-bearing premise

All reported contour sizes and figure-of-merit ratios scale from a single borrowed covariance matrix, estimated for a different data vector and redshift model than the one this paper uses; if that matrix does not represent LSST Y10's real errors, every forecasted number in the paper shifts along with it.

Editorial extensions

If this is right

  • LSST Y10 cosmic shear alone is photo-z-limited: without informative priors on the redshift distribution, its ($\Omega_m$, $\sigma_8$) and ($w_0$, $w_a$) contours grow by 3.8x and 6.3x, so external spectroscopic calibration becomes a requirement rather than a refinement.
  • The 3x2pt combination is more robust (3.4x and 3.2x) because galaxy clustering and galaxy-galaxy lensing partially self-calibrate the source photo-z parameters, so the added probes buy direct insurance against redshift error.
  • Calibration effort should follow the decision-tree ranking: secure the mean redshift of source bin 4 to protect $S_8$, and the bias and variance of bin 2 to protect $\Omega_m$, $\sigma_8$, and $w_0$.
  • Concrete training-set targets emerge: figures of merit increase monotonically with the number of spectroscopic galaxies, and the full bias+variance+outlier model is preferred only when the training set represents $z > 1.6$ galaxies at better than 50-70 per cent completeness.
  • If the photo-z model is wrong rather than merely unknown, the forecast predicts roughly 2-3.4 sigma biases in $\Omega_m$, $\sigma_8$, $w_0$, and $w_a$, with the exact shifts depending on the true error values.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper keeps the outlier shape $n_{\mathrm{out}}(z)$ fixed while marginalizing only its fraction; if the true outlier distribution has a different shape, the effective means and widths shift in a way the 15-parameter model cannot absorb, so the real contour inflation for deep samples could exceed the reported factors.
  • FisherA2Z is survey-agnostic, so the same 15-parameter machinery could be pointed at Year 1, at Roman, or at Euclid-style setups; a natural first test is rerunning the decision-tree ranking for LSST Y1, where the paper notes there are fewer usable lens-source bin pairs, to see whether the bin-4/$S_8$ sensitivity persists when self-calibration is weaker.
  • The bias forecast is first-order, and the authors themselves warn that Eq. (13) overestimates cosmological bias because a full MCMC would shift the nuisance posteriors toward the biased values; a sampling run with the same model would likely soften the 2-3.4 sigma bias claims while leaving the contour-inflation factors largely intact.
  • The bin-level rankings imply an observational program: prioritize deep spectroscopic coverage of the $z \sim 1$-$1.5$ galaxies that populate source bin 4 for $S_8$, rather than spreading calibration galaxies uniformly across redshift.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 6 minor

Summary. The paper presents FisherA2Z, an open-source Fisher forecasting code for LSST Y10 3x2pt and cosmic-shear analyses, built around a 15-parameter photometric redshift model (bias, variance, and outlier rate per tomographic bin), a four-parameter NLA intrinsic-alignment model, and ten lens galaxy bias parameters. It reports that marginalizing over the 15 photo-z parameters enlarges the 2-sigma confidence contours by factors of 1.9-3.4 for 3x2pt and 2.5-6.3 for cosmic shear depending on the parameter plane, identifies via decision-tree feature importance which photo-z parameters matter most for each cosmological parameter (notably bin 4 mean redshift for S8 in 3x2pt), and forecasts how spectroscopic training-set size and high-redshift completeness improve the figures of merit. The code is validated against the DESC-SRD forecast to within about 20 percent in the figures of merit (Appendix A).

Significance. If the forecasts hold, the paper is a useful and timely contribution: it provides a public, tested forecasting tool, a systematic treatment of a more realistic photo-z error model than the DESC-SRD baseline, and concrete guidance on which tomographic bins and photo-z parameters most need calibration. The open-source code, the explicit validation against DESC-SRD, and the decision-tree sensitivity analysis are concrete strengths, as are the training-set scenario forecasts and the Bayes-factor model comparison. The qualitative conclusion that 3x2pt partially self-calibrates photo-z uncertainties while cosmic shear is more strongly degraded is well supported. However, the quantitative headline numbers for the cosmic-shear-only case are prior-sensitive, and the covariance transfer from the DESC-SRD is an upstream assumption; both require attention before the specific numerical claims can be taken at face value.

major comments (2)
  1. [Section 3.1, Figure 4, and Appendix C, Table C1] The paper claims in Appendix C that 'the choice of prior width does not affect the overall conclusion' and in Section 3.1 that 'the posteriors for the photo-z parameters are significantly narrower than their priors.' For the cosmic shear analysis, Table C1 reports a likelihood-only 1-sigma posterior of 0.15 for delta_z5, the mean-redshift bias of the highest source bin, which is 50 percent larger than the assumed Gaussian prior sigma = 0.1. For this parameter the prior is more informative than the data, so the marginalized cosmic-shear contour sizes, including the headline enlargement factors of 3.8 in (Omega_m, sigma_8) and 6.3 in (w0, wa), depend on the prior width. Please re-run the cosmic-shear forecasts with a wider or flat prior for delta_z5 (and check for correlated high-z parameters), or explicitly qualify the headline factors as prior-dependent and soften the claim that the prior choice does not affect the results.
  2. [Section 2.5] The covariance matrix is taken from the DESC-SRD 3x2pt forecast without re-derivation for the new data vector that includes the 15-parameter photo-z model and the FlexZBoost outlier distribution. All Fisher contour areas, and therefore every contour-enlargement factor and FoM ratio in the paper, scale directly with this covariance matrix. The Appendix A validation to within about 20 percent of the SRD FoM is reassuring for the no-photo-z-marginalization case, but it does not test whether the covariance remains valid when the 15 photo-z parameters and the outlier population are added to the forward model. Please add either a covariance recomputed analytically for the new data vector or a sensitivity study showing how the contour-enlargement factors change under a reasonable range of covariance models.
minor comments (6)
  1. [Section 4] The concluding paragraph states the paper uses 'a 36-parameter model incorporating four cosmological parameters,' but Section 2.6 lists seven cosmological parameters and the total is 7 + 4 + 15 + 10 = 36; please correct 'four' to 'seven.'
  2. [Section 2.2] The word 'refllective' should be 'reflective.'
  3. [Section 3.4] The phrase 'we randomly sample a 5000 redshift parameters' should read 'we randomly sample 5000 redshift parameter values.'
  4. [Appendix B] The sentence 'our main conclusion are unchanged' should read 'our main conclusions are unchanged.'
  5. [Section 2.7] The description of the joint training set could clarify how the 1000-by-1000 galaxy resampling translates into the 15-dimensional feature vector; the connection between the resampling procedure and the feature distributions is currently implicit.
  6. [Figure 4 caption] The caption states 'the results include marginalization over the remaining seven cosmological parameters,' but in the (Omega_m, sigma_8) plane only five other cosmological parameters are marginalized over; please correct the number.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: Fisher forecasts are self-contained forward-model calculations with external DESC-SRD inputs; the flagged delta_z5 prior-sensitivity is a robustness concern, not circularity.

full rationale

The paper's derivation chain is self-contained in the circularity sense. FisherA2Z constructs a 36-parameter Fisher matrix from CCL-based data vectors, numerical derivatives, and the DESC-SRD covariance; the headline contour-enlargement factors follow directly from marginalizing the inverted Fisher matrix (Eq. 12) with and without the 15 photo-z parameters. The photo-z parameters are inputs (Table 1), not quantities inferred from the paper's own outputs, and the factors are quoted as ratios of marginalized posterior areas. The decision-tree feature importance is an interpretability pass over the same forward model using Eq. 13, not a derivation of a result from its own input. Self-citations to the DESC-SRD provide covariance, fiducial values, and scale cuts as external assumptions, and Robertson et al. in prep is mentioned only as a comparison; neither functions as a load-bearing uniqueness argument. Per the reviewing rule, we explicitly flag one internal-consistency concern that is not circular: Appendix C asserts that self-constraints on all redshift parameters are 'significantly tighter than their prior distribution,' but Table C1 lists a cosmic-shear-only posterior width of 0.15 for delta_z5 against a prior sigma of 0.1, meaning that parameter is prior-dominated and the cosmic-shear contour factors are partially prior-dependent. This is a robustness/correctness issue, not a reduction of the prediction to its inputs by construction, so it does not raise the circularity score.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The central claim rests on the SRD covariance being transferable, the forward model being sufficiently accurate, and the FlexZBoost/CosmoDC2 outlier distribution being representative. The 15 free photo-z parameters are the object of study, but their fiducial values and prior widths are assumptions. There are no invented physical entities; the paper introduces FisherA2Z software instead.

free parameters (3)
  • 15 photo-z nuisance parameters (delta_z_i, sigma_i, f_out,i) = delta_z_i = 0, sigma_i = 0.065 to 0.1875, f_out,i = 0.15
    These are the subject of the analysis. They are nuisance parameters with chosen fiducial values. They are not fitted to data in the paper, but the fiducial values are assumptions. The prior widths (0.1) are chosen to be wide/uninformative.
  • Fiducial outlier rate 15 percent = 0.15 in every bin
    Chosen as a 'conservatively large estimate' based on the overall FlexZBoost outlier rate, not measured for LSST. The paper notes the real LSST golden sample rate is expected to be much lower. This value sets the fiducial outlier distribution and affects the marginalization forecasts.
  • Numerical derivative step size = 0.01 for most parameters
    Chosen to give stable derivatives, with stability verified between 0.001 and 0.02 and FoM changes under two percent. This is a numerical choice, included for completeness.
assumptions (7)
  • domain assumption The DESC-SRD covariance matrix remains valid for the new data vector and model.
    Section 2.5 uses the covariance from LSST Dark Energy Science Collaboration et al. 2018 without recomputation. The data vector, photo-z model, and parameter set differ from the SRD, yet the covariance is assumed unchanged.
  • standard math The Limber and flat-sky approximations hold for the angular power spectra.
    Equation 4 invokes the Limber approximation and flat-sky approximation, standard in 3x2pt forecasts.
  • domain assumption The Eisenstein-Hu transfer function and Halofit (Takahashi et al. 2012) nonlinear power spectrum are accurate enough for the forecast.
    Section 2.2 states the linear matter power spectrum uses Eisenstein-Hu and nonlinear uses Halofit, a standard choice but an approximation.
  • domain assumption Linear galaxy bias per lens bin is sufficient.
    Section 2.4 assumes the galaxy density field is a linear tracer of matter modulated by a per-bin bias, motivating conservative scale cuts.
  • domain assumption The Fisher information matrix and first-order bias formula (Eq. 13) are valid for the parameter displacements used.
    Section 2.6 notes Eq. 13 is a first-order Taylor expansion, accurate only for small biases. The paper uses convergence tests for the decision tree sampling, and explicitly warns that the Graham et al. bias estimates are overestimated.
  • domain assumption Lens photometric redshift distributions are precisely known and not marginalized.
    Section 2.2 explicitly assumes lens photo-z are precisely modeled and fixed. This is an acknowledged simplifying assumption.
  • ad hoc to paper The 15 percent fiducial outlier rate and FlexZBoost/CosmoDC2 outlier shape represent the LSST Y10 outlier population well enough.
    Section 2.1.2 chooses the outlier shape from FlexZBoost applied to CosmoDC2 with i-mag<26.5. The paper acknowledges this sample is likely not what will be used for LSST cosmological lensing, but claims it is conservative. Appendix B tests one alternative, i-mag<25.3, but no other photo-z algorithm or catalog is tested.

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Cite this review

Pith. "Pith review of Forecasting the Impact of Source Galaxy Photometric Redshift Uncertainties on the LSST $3\times2$pt Analysis." pith.science (2026). https://pith.science/paper/CUOVTP6I

@misc{pith2026250701374,
  author       = {Pith},
  title        = {Pith review of: Forecasting the Impact of Source Galaxy Photometric Redshift Uncertainties on the LSST $3\times2$pt Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CUOVTP6I}},
  note         = {Machine review of arXiv:2507.01374}
}
abstract

Photometric redshifts of the source galaxies are a key source of systematic uncertainty in the Rubin Observatory Legacy Survey of Space and Time (LSST)'s galaxy clustering and weak lensing analysis, i.e., the $3\times 2$pt analysis. This paper introduces a Fisher forecast code FisherA2Z for the LSST Year 10 (Y10) $3 \times 2$pt and cosmic shear analyses, utilizing a 15-parameter redshift distribution model, with one redshift bias, variance, and outlier rate per tomographic bin. FisherA2Z employs the Core Cosmology Library CCL to compute the large-scale structure power spectrum and incorporates a four-parameter nonlinear alignment model for intrinsic alignments. We evaluate the impact of marginalizing over redshift distribution parameters on weak lensing, forecast biases in cosmological parameters due to redshift errors, and assess cosmological parameter sensitivity to redshift systematic parameters using decision trees. The sensitivity study reveals that for LSST $3\times2$pt analysis, $S_8$ is most sensitive to the mean redshift of the fourth out of the five source tomographic bins, while other cosmological parameters possess different sensitivities. Additionally, we provide cosmological analysis forecasts based on different scenarios of spectroscopic training datasets. We find that the figures-of-merit for the cosmological results increase with the number of spectroscopic training galaxies, and with the completeness of the training set above $z=1.6$, assuming the redshift information comes solely from the training set galaxies without other external constraints.

Figures

Figures reproduced from arXiv: 2507.01374 by the authors.

Figure 1
Figure 1. Redshift distribution of the source galaxy sample: The solid curves show the redshift distributions for the five tomographic source redshift bins, including both the core and outlier redshift distributions. The distributions are normalized such that the core and outlier rate combined integrate to unity, with the outliers comprising 15 per cent of the population. The core distributions follow the Gaussian model in Se… view at source ↗
Figure 2
Figure 2. This figure compares the FlexZBoost photo–𝑧 for the CosmoDC2 extragalactic catalog with 𝑖–mag< 26.5, against the true redshifts of galax￾ies in that catalog; this catalog is used in the KDE to define the outlier populations in this work. The top panel shows a histogram of the true and photometric redshifts for the entire catalog, while the bottom panel shows a histogram of the outlier populations selected as describ… view at source ↗
Figure 3
Figure 3. The redshift distributions of the lens sample in ten equally–spaced tomographic bins, described in Section 2.2. Parameter Fiducial Value Prior 𝜎 Ω𝑚 0.3156 0.15 𝜎8 0.831 0.2 𝑤0 -1 0.8 𝑤𝑎 0 1.3 ℎ 0.6727 0.125 𝑛𝑠 0.9645 0.2 Ω𝑏 0.049 0.003 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: The 2𝜎 Fisher confidence sets in the (Ω𝑚, 𝜎8) and (𝑤0, 𝑤𝑎) planes, before and after marginalizing over the 15 photo–𝑧 parameters for the 3 × 2pt (upper two panels) and cosmic shear (lower two panels). The colors correspond to different models parameters that are margin…
Figure 5
Figure 5. Figure 5: A comparison between the 2𝜎 Fisher confidence sets for the single–probe cases and for 3 × 2pt in the (Ω𝑚, 𝜎8) and (𝑤0, 𝑤𝑎) planes. The colors correspond to different probes according to the legend. The solid contours are from joint probes, while dashed lines contours a…
Figure 6
Figure 6. Figure 6: A comparison between the 3 × 2pt constraints for the 2–dimensional confidence sets in the (Ω𝑚, 𝜎8) and (𝑤0, 𝑤𝑎) spaces for the case with fiducial values (blue contours) assumed in this paper, and the case with photo–𝑧 model found in Graham et al. 2020 (orange contours)…
Figure 7
Figure 7. Figure 7: MAFE metrics for LSST Y10 cosmic shear analysis. We find the MAFE decrease with by redshift bias bins, stays approximately unchanged for the standard deviation, and is more sensitive to outlier rates of the first and last tomographic bin. z1 z2 z3 z4 z5 1 2 3 4 5 fout,…
Figure 8
Figure 8. Figure 8: Feature importance for the cosmic shear analysis with the 𝑤0 − 𝑤𝑎 model. The top panel shows the importance metrics with all 15 redshift parameters as input, while the bottom panel shows the important metrics with redshift parameters grouped by types across redshift bi…
Figure 9
Figure 9. Figure 9: MAFE metrics for LSST Y10 3 × 2pt analysis. We find that MAFE of 3 × 2pt analysis stays relatively unchanged with redshift bias 𝛿𝑧, increase with redshift 𝜎, and are more sensitive to the ourlier rates of the first and last tomographic bin. z1 z2 z3 z4 z5 1 2 3 4 5 fou…
Figure 10
Figure 10. Figure 10: Feature importance for the 3 × 2pt analysis with the 𝑤0 − 𝑤𝑎 model. The top panel shows the importance metrics with all 15 redshift parameters as input, while the bottom panel shows the important metrics with redshift parameters grouped into three groups. MNRAS 000, 1…
Figure 11
Figure 11. Figure 11: 2–dimensional contour plot for the Fisher forecast of LSST Y10 cosmic shear only analysis with redshift priors corresponding to different numbers of galaxies in the spectroscopic training set for the photo–𝑧 estimator. 𝑁 = 0 corresponds to a totally uninformative prio…
Figure 12
Figure 12. Figure 12: Left: The Figure–of–Merit (FoM) gain for Ω𝑚 − 𝜎8 and 𝑤0 − 𝑤𝑎 plane compared to the scenario of 𝑁samples = 0, for LSST Y10 cosmic shear and 3 × 2pt experiments. The dashed horizontal lines on the right side show the FoM improves with 𝑁samples = ∞. Right: The Figure–of–…
Figure 13
Figure 13. Figure 13: The log Bayes factor comparing different models given different photo–𝑧 priors corresponding to 𝑁samples and R. “BVO”, “BV” and “B” stands for bias+variance+outlier, bias+variance, and bias model correspondingly. A positive Bayes factor between model A and B means mod…

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