{"id":"1da94ba5-d189-4413-9ef5-45d4c80c193b","arxiv_id":"2505.13399","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A Wiener filter applied to weak-lensing magnification maps reduces noise correlations between radial bins and yields cluster mass estimates consistent with unfiltered analysis.","lead":"This paper applies a Wiener filter to galaxy density maps to remove large-scale noise before measuring cluster masses from weak-lensing magnification. It shows the filtering reduces correlations between radial bins and could improve mass estimates for future deeper surveys.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The forward model for filtered profiles is unvalidated and is built from the same noise model as the filter itself, so the filtered/unfiltered mass consistency cannot detect a common bias; an end-to-end mock recovery test is needed.","rationale":"The reader's weakest assumption identifies the random-position noise power spectrum as the key uncertainty. I agree that this is a central element, but the more precise load-bearing issue is the unvalidated forward model, of which that noise spectrum is one shared ingredient. Because the Wiener filter is linear, a wrong noise spectrum mainly degrades optimality rather than biasing the mean filtered signal, provided the same filter is applied in the forward model and to the data. The danger is instead that the forward model does not reproduce all signal and noise components that survive filtering at cluster positions, and the paper provides no end-to-end test with known input masses. The filtered/unfiltered mass consistency in Fig. 8 cannot rule out a common bias because both analyses share the cluster signal model and the filtered analysis additionally shares the noise model with the filter construction. This concern does not change the overall verdict: the method is plausible and the data-level demonstration of reduced noise correlations is useful, but the paper should be conditional on a realistic mock validation rather than accepted on the strength of the current simplified simulations.","tokens_in":16208,"tokens_out":13648,"duration_ms":153909,"concrete_test":"Run an end-to-end recovery test on realistic mocks with known cluster masses (for example, Ulagam or Dark-Emulator mocks with HSC-like depth, masking, and CAMIRA-like cluster selection). Apply the full pipeline: convergence-map construction, Wiener filter built from random-position noise spectra, bootstrap covariance, and the Sect. 6 forward-modeled likelihood. Compare the recovered stacked log10M against the known input for both filtered and unfiltered analyses. If the filtered recovery is biased by more than the statistical uncertainty while the unfiltered recovery is unbiased, the forward model is not faithful and the central claim fails; if both recover the input within errors, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 6 states that the forward-modeled filtered profiles make the mass estimate unbiased 'provided our noise model describes accurately the observed data.' This condition is the load-bearing point, and it is not demonstrated. The noise power spectrum is estimated once, from 10,000 random positions (Sect. 5.1), and it is used twice: to construct the Wiener filter in Eq. 25 and to generate the noisy fields in the forward model of filtered profiles. Because the same possibly-wrong noise spectrum enters both the filter applied to data and the filter applied in the forward model, an error in that spectrum will not show up as a filtered-vs-unfiltered mass disagreement. The two mass estimates can be perfectly consistent while the forward model is coherently wrong. The real risk is that the forward model omits or misrepresents signal and noise components that are present at cluster positions: correlated large-scale structure around clusters, non-Gaussian small-scale galaxy clustering, survey-mask convolution and patch-edge effects, and cluster-to-cluster variations in the environment. The simulations in Sect. 3.4 are simplified Gaussian fields with no two-halo environment and no treatment of the real mask, and the authors themselves say that forecasts from these simulations would be 'overly optimistic.' Thus the central claim that the method yields unbiased masses and will improve constraints for deeper surveys is not yet secured by the evidence presented.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a Wiener-filtering method for cluster weak-lensing magnification maps, intended to remove spatially correlated large-scale noise before radial averaging. The filter is constructed from an NFW-based signal prior and a noise power spectrum estimated from random positions, and it is applied to 1-degree patches around 1155 CAMIRA clusters in HSC. The authors show that the filtered maps have substantially reduced off-diagonal radial-bin noise correlations, that the filtered and unfiltered stacked mass estimates are consistent (log10 M/M_sun = 14.10+0.15-0.22 vs 14.20+0.17-0.30), and that the filtered errors are slightly smaller. They argue that for deeper surveys, where shot noise is less dominant, the method will yield larger improvements.","tokens_in":16461,"tokens_out":8202,"duration_ms":84148,"significance":"If validated, this would be a useful and fairly general technique for suppressing large-scale structure noise in stacked cluster lensing measurements, applicable to both magnification and shear. The covariance formalism in Sect. 3.1 is standard, and the qualitative claim that Wiener filtering reduces radial-bin noise correlations is convincingly demonstrated in both idealized simulations (Fig. 3) and HSC data (Fig. 7). The HSC measurement is internally consistent, and the background selection and convergence-response treatment in Sect. 4 are careful. The main weakness is that the unbiasedness of the filtered mass estimate is not yet established: the forward model in Sect. 6 is unvalidated and shares its noise model with the filter, so the central methodological claim rests on an unproven condition. The projected improvement for deeper surveys is also not quantitatively supported by the simplified simulations.","major_comments":[{"comment":"The unbiasedness claim for the filtered mass estimate rests on the sentence: \"This forward-modelling approach means that our mass estimation is not biased, provided our noise model describes accurately the observed data.\" This condition is never demonstrated. The noise power spectrum estimated in §5.1 is used both to construct the Wiener filter (Eq. 25) and to generate the noisy fields in the forward model, so any error in that spectrum affects the filtered data and the filtered model coherently; agreement between filtered and unfiltered masses in §6 is therefore not a test of the noise model. The mock fields in §3.4 are Gaussian, omit the two-halo term, and do not include the real survey mask, and the authors themselves describe quantitative forecasts from them as \"overly optimistic.\" I would need an end-to-end recovery test, in which clusters of known mass are injected into realistic masked HSC-like fields and the full filtered pipeline is run, to support the central claim of unbiased mass estimation.","section":"§6, Eq. (35)"},{"comment":"The noise power spectrum is estimated by averaging over 10,000 random positions in the survey, but the filter is then applied to patches centered on CAMIRA clusters. Cluster positions are biased tracers of large-scale structure, so the noise at those positions includes the correlated two-halo environment described in §2.2 and possibly residual cluster-member contamination; the random-position average does not obviously capture these contributions. Because the same spectrum enters both the filter and the forward model, a cluster-environment-dependent error in the noise model is precisely the kind of systematic that would bias the filtered mass without producing a filtered/unfiltered inconsistency. A direct comparison of the power spectrum measured at cluster positions with the random-position estimate, or an explicit quantitative argument that the difference is negligible, is needed.","section":"§5.1 and §2.2"},{"comment":"The signal prior C1h is defined as the Fourier transform of an NFW convergence profile, but the paper does not specify the mass, concentration, and redshift (or stacking distribution) used to construct it, nor the exact procedure for setting the sub-2-arcmin region to 10^-5. The Wiener filter, and therefore the filtered data and the forward-modeled profiles, depends on these unspecified choices. A sensitivity test over a plausible range of NFW prior parameters and downweight scales is required to show that the mass estimate and the claimed error reduction are robust to this prior.","section":"§3.3, Eqs. (24)-(25)"},{"comment":"The conclusion that the error reduction will become larger with future deeper datasets is stated in the abstract and conclusions, but the only quantitative support is the simplified simulation of §3.4, which the authors explicitly caution would yield \"overly optimistic\" forecasts. No forecast is made with an HSC-like noise amplitude, source density, mask, or cluster redshift distribution. This claim should either be supported by a more realistic end-to-end simulation or softened to a qualitative expectation.","section":"§3.4 and §7"}],"minor_comments":[{"comment":"The Gaussian likelihoods are missing the factor -1/2 and the transpose in the exponent; as written, exp[(d_i - kappa_i) C^-1 (d_i - kappa_i)] is not a correctly normalized Gaussian exponent.","section":"§3.2, Eqs. (20)-(21)"},{"comment":"The sentence \"We also employed a magnitude cut on the i-band magnitude with 23.5 < i\" appears to have the inequality reversed; the text and Fig. 5 indicate the intended cut is i < 23.5.","section":"§4.2"},{"comment":"The phrase \"not in the least because\" should likely read \"not least because\" in the discussion of why estimating many cluster parameters is non-trivial.","section":"§3.2"},{"comment":"The subscript notation on C^n_total is inconsistent with the terms on the right-hand side, which all carry (i,j); the total covariance should be written C^n_total,ij, and the terms C^ulss_ij and C^clss_ij should be defined before or immediately in the equation.","section":"§3.1, Eq. (18)"},{"comment":"The text refers to \"six linearly spaced angular bins between 0.75 and 5.2 Mpc,\" mixing angular and physical units; the conversion using the mean cluster redshift should be stated explicitly to avoid ambiguity.","section":"§6"},{"comment":"The reference list contains two entries for Umetsu et al. 2014 with identical bibliographic data; one should be removed.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is a plausible methods contribution and the qualitative filtering result is interesting, but I would not accept it in the current form without the end-to-end mock recovery test described in the major comments. The authors' own caveat about \"overly optimistic\" simulations indicates awareness of the validation gap, and closing that gap is feasible within the scope of a revision. I found no concerns about novelty disclosure or citation practice beyond the duplicate reference noted in the minor comments."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nQuick take: this is a solid, honest methods paper. The genuinely new element is applying a Wiener filter built from an NFW signal prior to magnification maps before stacking for cluster mass estimation. It does what it claims: radial-bin noise correlations drop substantially in both the simplified simulations and the HSC data, and the filtered and unfiltered masses are consistent (posteriors at 14.10 and 14.20 in log10 M/M⊙, slightly tighter errors after filtering). The authors are upfront about where they cut corners — they warn that the simplified Gaussian simulations would give overly optimistic forecasts, and they explicitly flag the noise-model assumption in Sect. 6.\n\nCredit where due: the covariance formalism in Sect. 3.1 is standard and correctly applied; the background selection follows the Chiu et al. 2020 color cuts with a direct measurement of the magnification response (R = 1.54) and a useful comparison to the photo-z-selected sample; the random-position null test is the right calibration check; and they cite the related filtering approaches (sigma-clipping, truncated isothermal filters) rather than claiming novelty in a vacuum.\n\nWhere it's soft, in proportion:\n\nFirst, the validation gap the stress-test note flags is real. The forward model for filtered profiles is built from the same noise power spectrum — measured once from 10,000 random positions — that constructs the filter. If that noise model is wrong at cluster positions (two-halo environment, non-Gaussian small-scale clustering, mask effects), the filtered and unfiltered mass estimates can agree perfectly while sharing a common bias. The Sect. 3.4 simulations never include those complications, so the claim of unbiased masses is asserted, not demonstrated. The fix is concrete: an end-to-end mock recovery test with realistic mocks, cluster environment, and the actual survey mask.\n\nSecond, the HSC-level gain is marginal because shot noise dominates at current depth. The paper says so honestly; the forward-looking claim that deeper surveys will benefit is extrapolation from the mechanism, not evidence.\n\nThird, minor: no code or data products, no quantitative comparison to the simpler filters they cite, and the fiducial NFW parameters defining the signal prior are not stated.\n\nWho it's for: cluster-lensing methods people, particularly anyone planning stacked magnification analyses with Euclid or Rubin. It deserves a serious referee — the right outcome is review with a request for the mock recovery test, not a desk reject.","headline":"A credible, honest methods paper on Wiener filtering for stacked cluster magnification masses whose main validation gap — the forward model shares the filter's noise model — is real and fixable.","tokens_in":17003,"tokens_out":6494,"would_cite":true,"duration_ms":53534,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Wiener filtering the observed galaxy density field removes large-scale noise from cluster weak-lensing mass estimates.","keywords":["weak-lensing magnification","galaxy cluster masses","Wiener filter","noise covariance","cosmic variance","Hyper Suprime-Cam","CAMIRA clusters","NFW profile"],"falsifier":"Take the same 1155 clusters, measure their stacked shear profile (whose noise is largely independent of the magnification shot noise), and compare the shear-inferred mass to the filtered-magnification mass; a disagreement beyond the statistical error would indicate that the filter's noise model is wrong. A more direct test is to check that the filtered profiles around the 10,000 random positions have zero mean and that the empirical noise power measured at cluster positions matches the random-position estimate.","tokens_in":15987,"feed_emoji":"🔭","tokens_out":5296,"duration_ms":43764,"temperature":0.7,"pith_summary":"Cluster masses inferred from weak-lensing magnification are limited by noise that is spatially correlated across the survey, so simple radial averaging is not optimal. This paper introduces a Wiener filter that downweights the large-scale modes of the observed galaxy density field before measuring stacked magnification profiles, using the cluster NFW convergence profile as the signal prior and a noise power spectrum measured from random sky positions. Applied to 1155 CAMIRA clusters in the Hyper Suprime-Cam survey, the filter removes most of the correlation between radial magnification bins while leaving the estimated mass consistent with the unfiltered measurement. The authors argue that because the residual error is currently dominated by irreducible shot noise, the benefit is modest with HSC data but will grow for deeper surveys; the same technique applies to weak-lensing shear.","feed_headline":"Wiener filtering removes bin-correlated noise from cluster mass maps","feed_subtitle":"On 1,155 HSC clusters, filtered and unfiltered masses agree while radial-bin noise correlations shrink.","key_machinery":"The Wiener filter, Eq. (25): each Fourier mode of the observed galaxy density field is rescaled by $\\hat{\\kappa}_{\\ell m} = \\frac{C^{\\kappa}_{1h,\\ell}}{C^{\\kappa}_{1h,\\ell}+C^{n}_{\\ell}} d_{\\ell m}$, where $C^{\\kappa}_{1h,\\ell}$ is the angular power spectrum of the NFW convergence profile (the signal prior, with small scales below 2 arcminutes downweighted) and $C^{n}_{\\ell}$ is the noise power spectrum estimated by averaging 2D power spectra from 10,000 random sky positions. The filter removes both low-$\\ell$ modes from large-scale structure along the line of sight and high-$\\ell$ shot-noise-dominated modes. Because the filter changes the shape of the magnification profile, the paper forward-models filtered profiles from simulated noisy fields so that the mass estimate is unbiased.","core_discovery":"The central claim is that Wiener filtering the observed magnification field, weighting each Fourier mode by the ratio of the NFW one-halo signal power to the total signal-plus-noise power, produces a stacked cluster magnification profile whose radial bins have substantially lower noise correlations than unfiltered profiles, with no loss of constraining power. The paper demonstrates this in two ways: simulated magnification fields show a clear reduction in off-diagonal covariance, and HSC data show the same effect. Mass estimates from filtered and unfiltered fields are consistent (log10 M/Msun = 14.10+0.15-0.22 vs 14.20+0.17-0.30), with the filtered posterior slightly tighter. The method is presented as a simplification of a full field-level maximum-a-posteriori estimate, and the authors emphasize that forward-modelling the filtered profile is required to avoid bias.","pith_inferences":["If the method scales to individual clusters rather than stacks, it could turn the mass-richness relation itself into a field-level estimate, which the paper sketches in Sect. 3.2 but does not implement.","The filter's signal prior is derived from an NFW profile with a fixed concentration; allowing the prior to vary with richness or redshift might recover some of the two-halo signal that the current filter removes, at the cost of reintroducing covariance.","The testable prediction that deeper surveys will see larger gains could be checked by running the same pipeline on simulated deep surveys before real data arrive.","If dust extinction is non-negligible, the magnification response R differs by band; the filter would then need a multi-band extension, which the paper identifies but does not pursue."],"forward_implications":["Noise correlations between radial magnification bins are significantly reduced by the filter, making the stacked signal closer to a diagonal-covariance measurement.","Filtered and unfiltered mass estimates agree, so the method adds no detectable bias at the current precision.","For deeper surveys with smaller shot noise, the relative improvement in mass uncertainty should grow because the correlated large-scale noise becomes the dominant error.","The same Wiener filter construction is directly applicable to weak-lensing shear fields.","Because the filter suppresses large-scale survey modes, it can relax requirements on survey uniformity for magnification-based mass estimates."],"supporting_citations":[{"why":"Supplies the optimal filter formalism used to derive Eq. (25).","marker":"Wiener 1949"},{"why":"Defines the NFW profile used as the signal prior and mass model.","marker":"Navarro et al. 1997"},{"why":"Provides the colour-cut background selection and the comparison dataset for magnification-based cluster masses.","marker":"Chiu et al. 2020"},{"why":"Presents the CAMIRA cluster catalogue used to select the 1155 clusters.","marker":"Oguri et al. 2018"},{"why":"Introduces the cosmic-variance noise contribution to cluster mass measurements that the filter targets.","marker":"Hoekstra 2003"},{"why":"Models the correlated large-scale structure (two-halo) noise contribution to the covariance.","marker":"Gruen et al. 2015"},{"why":"Supplies the analytic projected NFW surface-density profiles used for the one-halo signal.","marker":"Wright & Brainerd 2000"},{"why":"Provides the halo-bias relation used to fix the two-halo term in the mass model.","marker":"Tinker et al. 2010"}],"fun_headline_variants":["Wiener filter cuts radial-bin noise ties in cluster mass maps","Cluster masses stay put as Wiener filter cleans magnification noise","Filtering large-scale noise sharpens cluster mass estimates","New filter trims noise correlations in cluster lensing analyses","Wiener filtering improves cluster mass precision for deep surveys"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The noise power spectrum measured from 10,000 random positions is an unbiased, stationary, Gaussian description of the noise at the cluster positions; if it is not, the filter will not remove the right modes and the forward-modelled mass estimate could be biased.","fun_headline_variants_meta":{"raw":{"variants":["Wiener filter cuts radial-bin noise ties in cluster mass maps","Cluster masses stay put as Wiener filter cleans magnification noise","Filtering large-scale noise sharpens cluster mass estimates","New filter trims noise correlations in cluster lensing analyses","Wiener filtering improves cluster mass precision for deep surveys"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000644,"raw_usage":{"total_tokens":2951,"prompt_tokens":925,"completion_tokens":2026,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":541,"completion_tokens_details":{"reasoning_tokens":1947}},"tokens_in":541,"tokens_out":2026,"duration_ms":14399,"temperature":1.0,"reasoning_tokens":1947,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:14:42.521007+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the same 1155 clusters, measure their stacked shear profile (whose noise is largely independent of the magnification shot noise), and compare the shear-inferred mass to the filtered-magnification mass; a disagreement beyond the statistical error would indicate that the filter's noise model is wrong. A more direct test is to check that the filtered profiles around the 10,000 random positions have zero mean and that the empirical noise power measured at cluster positions matches the random-position estimate.","supporting_citations":[{"cited_title":"1949, Extrapolation, Interpolation, and Smoothing of Stationary Time Series: With Engineering Applications (Cambridge, MA: MIT Press)","cited_arxiv_id":null,"evidence_quote":"Supplies the optimal filter formalism used to derive Eq. (25)."},{"cited_title":"2020, MN- RAS, 495, 428","cited_arxiv_id":null,"evidence_quote":"Provides the colour-cut background selection and the comparison dataset for magnification-based cluster masses."},{"cited_title":"2015, MNRAS, 449, 4264","cited_arxiv_id":null,"evidence_quote":"Models the correlated large-scale structure (two-halo) noise contribution to the covariance."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the analytic projected NFW surface-density profiles used for the one-halo signal."}],"review_version":1}