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The DESI-Lensing Mock Challenge: large-scale cosmological analysis of 3x2-pt statistics

T0 review · 3 major / 3 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper shows that a full mock-based analysis pipeline for DESI Year 1 lensing and clustering data recovers the input cosmology within the statistical error margins.

desk verdict Solid mock challenge for the DESI-Y1 3x2-pt pipeline; the new wp covariance is the key ingredient and the one part not directly mock-validated. read the letter →

arxiv 2412.12548 v2 pith:M5RZ3ANY submitted 2024-12-17 astro-ph.CO

C. Blake , C. Garcia-Quintero , S. Ahlen , D. Bianchi , D. Brooks , T. Claybaugh , A. de la Macorra , J. DeRose
show 36 more authors
A. Dey P. Doel N. Emas S. Ferraro J. E. Forero-Romero G. Gutierrez S. Heydenreich K. Honscheid C. Howlett M. Ishak S. Joudaki E. Jullo R. Kehoe D. Kirkby A. Kremin A. Krolewski M. Landriau J. U. Lange A. Leauthaud M. E. Levi M. Manera R. Miquel J. Moustakas G. Niz W. J. Percival I. Pérez-Ràfols A. Porredon G. Rossi R. Ruggeri E. Sanchez C. Saulder D. Schlegel D. Sprayberry Z. Sun G. Tarlé B. A. Weaver
This is my paper · ORCID
classification astro-ph.CO
keywords 3x2-ptcorrelationfunctionsweakgravitationallensingprojectedfunctionanalyticalcovariancesuper-sampleDESIYear1cosmologicalparameterrecoverymockchallenge
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

This paper is an end-to-end dress rehearsal for the combined analysis of DESI Year 1 galaxy clustering with weak lensing data from KiDS, DES, and HSC. The authors build realistic mock catalogues from N-body simulations, compute the full analytical covariance of the 3x2-pt correlation functions, and fit the mock data with a Bayesian pipeline. Their central claim is that the fiducial cosmological parameters of the simulation are recovered within the statistical error margin of the experiment, meaning the pipeline is unbiased at the precision DESI-Y1 will deliver. The new ingredient is the analytical covariance attached to the projected correlation function $w_p(R)$ and its cross-correlations with the shear statistics, which has not been validated against the mock ensemble because the simulations cannot provide a reliable numerical covariance for it.

What carries the argument

The central object is the analytical covariance matrix of the combined 3x2-pt data vector. It is built from Gaussian, noise, and super-sample contributions following the formulations of Krause & Eifler and Joachimi et al., with a new extension: the covariances between the projected correlation function $w_p(R)$ and the angular shear statistics $\xi_\pm(\theta)$ and $\gamma_t(\theta)$, derived in the Limber approximation in Appendix D. This machinery sets the error bars in the parameter fits; the validation of the shear and galaxy-galaxy lensing diagonal errors against the mock ensemble, agreeing to a few percent, is what gives the parameter-recovery claim its weight.

What would settle it

A direct check would be to compare the analytical $w_p(R)$ covariance to the scatter of $w_p$ measurements across a suite of mock catalogues built without the domain-decomposition artefact or with that effect corrected; if the analytical errors deviate from the mock scatter by more than the few-percent level seen for $\xi_\pm$ and $\gamma_t$, the parameter-recovery claim would be undermined. A cheaper test is to check whether $w_p$-only fits across many realisations produce a $\chi^2$ distribution consistent with the assumed number of degrees of freedom.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that the 3x2-pt pipeline for DESI-Y1, combining cosmic shear $\xi_\pm$, galaxy-galaxy lensing $\gamma_t$, and projected clustering $w_p$, is ready for real data: fits to simulated data vectors return the input values of $\Omega_m$ and $S_8$ within roughly half a $\sigma$ to one $\sigma$, with probability-to-exceed statistics comparable to earlier DES-Y3 validation. The parameter biases in the fitted data are consistent with the noise expected from eight mock realizations plus prior volume effects. The paper therefore concludes that the fiducial fitting configuration produces an acceptable recovery of the underlying cosmology at DESI-Y1 precision.

Load-bearing premise

The analytical error model for the projected clustering measurement and its correlation with the shear measurements is assumed to be correct, but it could not be checked directly against the simulated data because the simulations' domain decomposition spoils the numerical covariance estimate for $w_p$.

Editorial extensions

If this is right

  • The DESI-Y1 3x2-pt analysis can proceed using the analytical covariance, including the new $w_p$ cross-terms, without needing a large mock ensemble to calibrate the error matrix.
  • Cosmic shear alone recovers the fiducial parameters with the smallest bias, while the galaxy-galaxy lensing plus clustering combination shows somewhat larger, though still acceptable, biases, meaning the choice of small-scale cuts matters.
  • Including the projected correlation function of the spectroscopic lenses adds clustering signal-to-noise without degrading the cosmological parameter recovery.
  • The validated framework directly supports the upcoming joint DESI-Y1, KiDS, DES and HSC cosmology analysis.

Reading between the lines

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

  • The $w_p$ covariance, being the one part of the error model not directly checked against the mock ensemble, carries residual risk: if the true noise or super-sample terms for projected clustering are misestimated, the reported parameter errors on the clustering component would be off by that amount.
  • Because the mocks omit intrinsic alignments and other astrophysical effects, this validation establishes a floor on pipeline performance rather than a guarantee that real-data fits will be unbiased at the same level.
  • The same analytic covariance machinery is the natural foundation for the paper's stated next step, a joint analysis with full 3D clustering including redshift-space distortions, where the added growth-rate information would enter through new cross-covariance terms.
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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

3 major / 3 minor

Summary. This paper presents an end-to-end validation of the DESI-Y1 3x2-pt cosmological analysis pipeline using the Buzzard N-body simulation suite. The authors construct mock galaxy and weak lensing catalogs matching DESI BGS/LRG lenses and KiDS-1000, DES-Y3, and HSC-Y1 sources, measure cosmic shear xi±(theta), galaxy-galaxy lensing gamma_t(theta), and projected clustering wp(R), and compute an analytic covariance including Gaussian, super-sample, and noise terms, with new cross-covariance terms involving wp(R) derived in Appendix D. The covariance is tested against the mock ensemble for xi± and gamma_t and against two external codes for xi± and gamma_t; cosmological parameter recovery is then tested with CosmoMC using fiducial scale cuts Rclus=7 h^-1 Mpc and Rggl=10 h^-1 Mpc, with the third lens bin excluded. The paper reports parameter biases in the Omega_m-S8 plane below about 1 sigma and concludes that the fiducial 3x2-pt configuration recovers the underlying cosmology within the statistical error appropriate for DESI-Y1.

Significance. If correct, the paper would provide a valuable end-to-end validation of a key analysis pipeline and introduces a new analytic ingredient—the cross-covariance between the projected correlation function and angular shear/GGL statistics—that will be used in the DESI-Y1 analysis. The strengths include the realistic mock construction, the detailed analytic covariance formalism, the public data release for the figures, and the explicit comparison to external covariance codes at the 1% level for the angular statistics. However, the central validation claim is weakened by the admitted lack of a direct mock-based test of the wp covariance block, which is a principal new ingredient and an input to the parameter-recovery likelihood. The paper is therefore a solid methodological contribution whose headline claim requires an additional validation step before it can be taken as fully demonstrated.

major comments (3)
  1. [Sec. 3.2, Apps. D-E] The analytic covariance for wp(R) and its cross-covariances is not directly validated against the Buzzard ensemble; Sec. 3.2 states this explicitly, and the external-code comparisons in Appendix E cover only the xi± and gamma_t configurations, not the wp block or its cross-terms. The global chi^2 and PTE statistics used in Secs. 5.5-5.6 are integrated quantities that cannot localize a block-specific error in the wp covariance, and because the same covariance enters both the data and fiducial-model fits in Eq. (21), a block-specific miscalibration would directly affect the reported 'within statistical error margin' statement. Since the headline claim rests on this likelihood ingredient, a direct validation of the wp covariance (e.g., against an alternative simulation without the domain-decomposition issue, or against an independent analytic code including the wp block) is needed.
  2. [Sec. 5, Sec. 5.6] The third lens redshift bin (0.3<z<0.4) is excluded from all fits because of the Buzzard light-cone transition, as stated in Sec. 5, but the abstract and Sec. 5.6 present the recovery claim without this qualification. The validation is therefore performed on four lens bins rather than the five-bin DESI-Y1 configuration, so the headline claim is stronger than the test actually performed. The paper should state this exclusion explicitly wherever the 'within statistical error' claim is made and, ideally, quantify the impact of the excluded bin on the reported biases.
  3. [Sec. 2.1 and Sec. 3.1] The analytic covariance is computed using fiducial linear bias factors b=(1.35,1.51,1.65,2.21,2.44) that are fitted to the mock projected correlation functions, while the same wp data are later analyzed in the likelihood with galaxy bias parameters that are free. This partial dependence of the covariance on the analyzed data introduces a potential circularity that is not quantified; the paper should test the sensitivity of the parameter-recovery conclusions to the bias values assumed in the covariance, for example by repeating the fiducial fit with bias parameters shifted by their fitted uncertainties.
minor comments (3)
  1. [Sec. 5.1] The maximum wp scale cut is set to half the projected separation of the average nside=8 pixel size; this is an ad hoc choice and a sensitivity test varying this cut (e.g., to one-third or two-thirds of the pixel scale) would strengthen the scale-cut validation.
  2. [Eq. (21)] The PTE definition invokes a rescaling of the covariance by the number of mock realizations M, but the exact form of the rescaled covariance C^M is not written out; specifying this rescaling explicitly would improve reproducibility.
  3. [Fig. 17] The individual lens redshift bins are not labeled directly in the panels of Fig. 17; adding the redshift ranges to each panel would improve readability.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the parameter-recovery claim is an empirical end-to-end test, and the covariance derivation is independent of the claimed result.

full rationale

The central claim, recovery of the Buzzard fiducial cosmology within statistical errors, is tested by fitting mock data vectors with a likelihood whose covariance is derived analytically from standard power-spectrum covariance formulas (Krause & Eifler 2017; Joachimi et al. 2021) and presented in Appendices A–D. The galaxy bias values used in the covariance are fitted from the mock projected correlation functions (Sec. 2.1), but they enter only the error normalization; the cosmological parameters are free, and the recovery of Omega_m and S8 is not statistically forced by these inputs. The analytical covariance is checked against external codes for the xi+/- and gamma_t blocks (Appendix E) and against mock dispersion for xi+/- and gamma_t (Sec. 3.2); the admitted lack of a direct mock comparison for the wp block (Sec. 3.2) is a validation gap, not a circular reduction. The PTE statistic compares mock-mean fits to fiducial-model fits using the same covariance, which is an internal consistency test rather than a construction of the result. The fiducial scale cuts were chosen after inspecting mock fits (Secs. 5.1 and 5.5), which introduces some selection, but the paper also reports results for alternative cuts, so the recovery statement is not a tautology. Self-citations (e.g., DeRose et al. 2019, 2022) are used as prior validation or comparison, not as the load-bearing justification for the recovery claim.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The central claim depends on the Buzzard mocks being representative of the real surveys, on the analytical covariance being accurate (including the unvalidated wp cross-terms and the assumed-negligible non-Gaussian part), and on scale cuts chosen to make the linear bias model valid. These are inputs from prior work or by hand rather than derived in this paper.

free parameters (4)
  • Galaxy bias factors b_i in covariance = (1.35, 1.51, 1.65, 2.21, 2.44)
    Adopted for the covariance calculation based on fits to the mock projected correlation functions (Sec 2.1); the covariance then depends on these fitted values.
  • Lens magnification coefficients alpha_i = (0.91, 1.58, 2.02, 2.58, 2.26)
    Fixed to values measured from the Buzzard mocks (Sec 4.2.4, Table 1); not fitted in the likelihood but used as inputs.
  • Fiducial scale cuts Rggl, Rclus = Rggl = 10, Rclus = 7 h^-1 Mpc
    Chosen based on linear bias validity and the mock fit performance (Sec 5.1, 5.5); variations to 6 and 10 are tested, so the fiducial choice is informed by the same data being validated.
  • Large-scale wp cut (domain decomposition bound) = half the projected separation of the average angular size of nside=8 pixels
    A hand-set maximum scale cut for wp to remove Buzzard domain decomposition effects (Sec 5.1).
assumptions (7)
  • domain assumption The Buzzard mocks faithfully reproduce the lens and source redshift distributions, weights, photo-z errors, shear calibration and magnification of the real surveys (Sec 2.1).
    The mocks are drawn with ADDGALS and HOD recipes matched to DESI EDR and to KiDS/DES/HSC source properties; if any of these matches are inaccurate, the validation may not transfer to real data.
  • domain assumption Intrinsic alignments are absent from the mocks and therefore from the validation (Sec 2.1).
    The real-data analysis will marginalise over intrinsic alignment models (Porredon et al. in prep), but this pipeline test does not exercise that part of the model.
  • domain assumption The non-Gaussian (connected) covariance is negligible for this 3x2-pt data vector (Sec 3.1, 'We do not include the non-Gaussian contribution ... (Joachimi et al. 2021)').
    This is a cited assumption, not tested here; if non-Gaussian terms are significant, the error bars are underestimated.
  • domain assumption The linear Kaiser bias model with a constant bias per bin is adequate at the chosen scale cuts (Sec 4.2.3).
    The scale cuts are designed to make this true, but the paper shows residual model-data differences on small scales (Fig 5, 6); if the cuts are insufficient, parameter biases could be larger than reported.
  • domain assumption Buzzard's matter power spectrum and halo model reproduce the true lensing and clustering signals (halofit shown to reproduce Buzzard cosmic shear in DeRose et al. 2019).
    The fiducial cosmology is recovered relative to Buzzard's own input, but if Buzzard itself is not a perfect representation of the universe (e.g., resolution limits, domain decomposition), the validation does not catch those errors.
  • ad hoc to paper The third lens redshift bin (0.3 < z < 0.4) is excluded from all fits because of the Buzzard light-cone transition (Sec 5).
    This is a simulation-specific exclusion; it removes a redshift range present in the real DESI-Y1 data from the validation.
  • ad hoc to paper The maximum wp scale cut, set to half the projected separation of the mean nside=8 pixel size, removes domain decomposition effects (Sec 5.1).
    The cut value is estimated from the simulation's domain structure, not from data; if the estimate is wrong, large-scale clustering systematics leak into the fit.

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Cite this review

Pith. "Pith review of The DESI-Lensing Mock Challenge: large-scale cosmological analysis of 3x2-pt statistics." pith.science (2026). https://pith.science/paper/M5RZ3ANY

@misc{pith2026241212548,
  author       = {Pith},
  title        = {Pith review of: The DESI-Lensing Mock Challenge: large-scale cosmological analysis of 3x2-pt statistics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/M5RZ3ANY}},
  note         = {Machine review of arXiv:2412.12548}
}
read the original abstract

The current generation of large galaxy surveys will test the cosmological model by combining multiple types of observational probes. Realising the statistical promise of these new datasets requires rigorous attention to all aspects of analysis including cosmological measurements, modelling, covariance and parameter likelihood. In this paper we present the results of an end-to-end simulation study designed to test the analysis pipeline for the combination of the Dark Energy Spectroscopic Instrument (DESI) Year 1 galaxy redshift dataset and separate weak gravitational lensing information from the Kilo-Degree Survey, Dark Energy Survey and Hyper-Suprime-Cam Survey. Our analysis employs the 3x2-pt correlation functions including cosmic shear and galaxy-galaxy lensing, together with the projected correlation function of the spectroscopic DESI lenses. We build realistic simulations of these datasets including galaxy halo occupation distributions, photometric redshift errors, weights, multiplicative shear calibration biases and magnification. We calculate the analytical covariance of these correlation functions including the Gaussian, noise and super-sample contributions, and show that our covariance determination agrees with estimates based on the ensemble of simulations. We use a Bayesian inference platform to demonstrate that we can recover the fiducial cosmological parameters of the simulation within the statistical error margin of the experiment, investigating the sensitivity to scale cuts. This study is the first in a sequence of papers in which we present and validate the large-scale 3x2-pt cosmological analysis of DESI-Y1.

Figures

Figures reproduced from arXiv: 2412.12548 by the authors.

Figure 1
Figure 1. The weighted angular density per unit redshift of the mock Buzzard source samples used in our analysis, spanning different tomographic samples for the KiDS, DES and HSC datasets as divided by photometric redshift zp, and displayed as the solid lines. These densities are compared with those estimated for the survey datasets themselves using redshift calibration samples, and shown as the dotted lines. The “spikes” in … view at source ↗
Figure 2
Figure 2. The angular density per unit redshift of the mock Buz￾zard DESI samples used in our analysis, spanning three BGS and two LRG tomographic bins, displayed as the histograms. These densities are compared with the corresponding DESI Y1 sample, shown as the solid line. For the purposes of this study, the mocks do not contain incompleteness effects which are present in the Y1 sample, hence have a higher number density tha… view at source ↗
Figure 3
Figure 3. The division of each Buzzard simulation quadrant into multiple analysis regions corresponding to the representative overlap area of DESI-Y1 and KiDS-1000, DES-Y3 and HSC-Y1. Each quadrant is divided into 20 KiDS regions, 12 DES regions and 60 HSC regions, corresponding to 9, 15 and 3 pixels of a Healpix nside = 8 pixelisation, respectively. The different segmentations used to represent each weak lensing survey are d… view at source ↗
Figures from the paper (14 more)
Figure 4
Figure 4. Figure 4: The cosmic shear correlation functions (ξ+, ξ−) between the five tomographic source samples of the KiDS-1000 Buzzard mocks, as a function of angular separation θ in arcminutes. The different panels display measurements for different combinations of tomographic samples,…
Figure 5
Figure 5. Figure 5: The average tangential shear γt of the five tomographic source samples of the KiDS-1000 Buzzard mocks, around the five lens samples of the DESI Buzzard mocks, as a function of angular separation θ in arcminutes. The different panels display measurements for different c…
Figure 6
Figure 6. Figure 6: The projected correlation function wp of the five lens samples of the DESI Buzzard mocks, as a function of projected separation R in units of h−1 Mpc. We plot the mean and standard deviation of the measurements across the Buzzard KiDS regions. Shaded sections of panels…
Figure 7
Figure 7. Figure 7: The error in the shear correlation function measurements (ξ+, ξ−), denoted σ(ξ+) and σ(ξ−), between the five tomographic source samples of the KiDS-1000 Buzzard mocks, as a function of angular separation θ in arcminutes. The different panels display measurements for di…
Figure 8
Figure 8. Figure 8: The error in the average tangential shear γt of the five tomographic source samples of the KiDS-1000 Buzzard mocks, around the five lens samples of the DESI Buzzard mocks, as a function of angular separation θ in arcminutes. The different panels display measurements fo…
Figure 9
Figure 9. Figure 9: The correlation matrix corresponding to the combined-probe covariance of the 3×2-pt correlation function measurement of the KiDS-1000 and DESI Buzzard mocks. The measurements use Ntom = 5 source tomographic samples and Nlens = 5 lens samples. The analytical covariance …
Figure 10
Figure 10. Figure 10: The correlation coefficient of the off-diagonal combined-probe covariance matrix corresponding to KiDS-1000 and the DESI Buzzard mocks, r(i, j) = Cij/ p Cii Cjj . The differ￾ent panels display the full set of correlation coefficients for matrix elements sharing the sa…
Figure 11
Figure 11. Figure 11: 1σ and 2σ confidence contours derived from cosmic shear cosmological fits, represented in the projections of Ωm-S8 (top row) and Ωm-σ8 (bottom row). The blue contours represent the fits to a synthetic data vector generated using the fiducial cosmology of the Buzzard s…
Figure 12
Figure 12. Figure 12: 1σ and 2σ confidence contours derived from cosmological fits to a γt(θ) + wp(R) data vector representing the fiducial model (blue contours) and the mock mean (red contours). These results use scale cuts Rclus = 7 h−1 Mpc and Rggl = 10 h−1 Mpc and are displayed in the …
Figure 13
Figure 13. Figure 13: 1σ and 2σ confidence contours derived from cosmological fits to a 3 × 2-pt data vector representing the fiducial model (blue contours) and the mock mean (red contours). These results use scale cuts Rclus = 7 h−1 Mpc and Rggl = 10 h−1 Mpc, and the same cosmic shear sca…
Figure 14
Figure 14. Figure 14: The results of a code comparison between our analytical covariance and the evaluations of two external codes: CosmoCov (left￾hand panels) and the KiDS covariance code (right-hand panels). The comparison with CosmoCov includes the ξ±(θ) and γt(θ) correlations, and the …
Figure 15
Figure 15. Figure 15: The mock mean ξ± measurements and best-fitting models for the 3 × 2-pt fits. Each panel shows the measured correlation function for a combination of tomographic source bins averaged over 8 Buzzard mocks including overlapping and non-overlapping regions corresponding t…
Figure 16
Figure 16. Figure 16: The mock mean γt measurements and best-fitting models for the 3 × 2-pt fits, presented in the same style as Fig.15. Each panel shows the results for a combination of source bin (rows) and lens bin (columns). The same scale cuts are used for the three lensing surveys, …
Figure 17
Figure 17. Figure 17: The mock mean wp measurements and best-fitting models for the 3 × 2-pt fits, presented in the same style as Fig.15. The separate panels represent the five different DESI lens bins from low redshift (top) to high redshift (bottom). The excluded separations are represen…

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.