REVIEW 4 major objections 5 minor 42 references
The paper shows that the shape of the redshift bin—not just its width—controls how faithfully the transverse BAO scale is recovered, and that a hybrid semi-Gaussian bin outperforms Gaussian and top-hat bins for low-redshift surveys.
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 →
T0 review · deepseek-v4-flash
2026-08-03 20:44 UTC pith:LLZOMAZR
load-bearing objection A useful first systematic comparison of bin shapes for transverse BAO forecasts, but the headline semi-Gaussian recommendation rests on a hand-picked shape and no sensitivity scan, so it is a plausible guideline, not an established result. the 4 major comments →
On the bin sensitivity of the transverse BAO
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The central claim is that a redshift bin whose selection function is flat over 80% of the distribution and Gaussian-peaked over the remaining 20%—the 'semi-Gaussian' scheme with A=0.2, B=0.8, σ̃_z=0.01—recovers the transverse BAO peak closest to the fiducial value for SKA-like low-redshift surveys, and gives tighter or comparable parameter constraints than pure Gaussian or top-hat bins, despite higher shot noise. For DESI, semi-Gaussian is tightest below σ_z=0.04 and marginal otherwise. The proposed correction, θ_BAO = (1−α⁻−α⁺)θ_fit, uses the fiducial BAO angular scale of the two adjacent half-bin redshifts to remove the projection effect.
What carries the argument
The comparison hinges on three bin window functions: the Gaussian bin n_i(z) of Eq. 3.9 with width σ_z; the top-hat and semi-Gaussian bins ñ_i(z) of Eq. 3.10, which are flat at height A with a Gaussian bump of width σ̃_z on top; the semi-Gaussian case uses A=0.2, B=0.8, σ̃_z=0.01, and the widths are matched so the Gaussian σ_z is half σ̃_z. The correction mechanism is the adjacent-redshift formula in Eq. 5.1: θ_BAO = (1−α⁻−α⁺) θ_fit, where α⁻ and α⁺ are fractional deviations of the BAO scale at the lower and upper half-bin redshifts from the central value.
Load-bearing premise
The entire ranking assumes that the three bin shapes have the same effective full width (Gaussian σ_z set to half σ̃_z) and that the hand-picked semi-Gaussian parameters A=0.2, B=0.8, σ̃_z=0.01 are the right hybrid; if that width-matching rule or parameter choice is changed, the ordering of bin shapes could change.
What would settle it
A focused calculation varying the semi-Gaussian mixing fraction A from 0 to 1 (and the width σ̃_z) while keeping the total bin width fixed: if the recovered θ_BAO deviation α stops being closest to 1 for some intermediate A (or if top-hat overtakes it), the paper's central conclusion loses support. Equivalently, applying the three bin schemes to a realistic mock catalog with known cosmology and checking which returns the input θ_BAO would settle it.
If this is right
- For low-redshift surveys like SKA, adopting semi-Gaussian bins should recover the transverse BAO scale with less bias than top-hat or Gaussian bins, at σ_z < 0.04.
- The statistical correction based on adjacent redshift halves can be applied to existing and future angular BAO measurements to remove part of the projection bias.
- Gaussian binning, though common, gives the least precise parameter constraints among the three schemes for SKA, and is weak for DESI at small σ_z.
- The optimal bin width for BAO detection depends on z_c, so fixed thin bins are not automatically optimal; this supports the recommendation to choose bin width based on the survey's redshift range.
Where Pith is reading between the lines
- Editorial inference: The A=0.2/B=0.8 split is not derived from first principles; a systematic scan over A and B would reveal whether the semi-Gaussian advantage is a genuine feature of the shape or an artifact of this one parameter choice.
- Editorial inference: The adjacent-redshift correction (Eq. 5.1) assumes the projection bias can be captured by just two half-bin redshifts; for very wide bins or steep N(z), a full integral over the bin may be needed, and the correction should be tested on mocks before use.
- Editorial inference: If confirmed, the result suggests that photometric surveys with large redshift uncertainties could improve BAO constraints by engineering selection functions closer to a semi-Gaussian, rather than relying on top-hat photo-z shells.
- Editorial inference: The Fisher framework assumes Gaussian likelihood and ignores non-Gaussian covariance; a full simulation-based covariance could alter the FoM ranking.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. This paper studies how the choice of redshift-bin window shape (Gaussian, top-hat, and a hybrid 'semi-Gaussian') affects the measured transverse BAO angular scale and Fisher-forecast cosmological parameter constraints for SKA HI and DESI LRG surveys. The authors compute angular correlation functions and power spectra for each bin shape over a range of widths, extract the BAO peak position, compare it to the fiducial θ_BAO, and propose a correction based on fiducial shifts at the two half-bin edges. They find that the semi-Gaussian bin yields the most accurate BAO position for σ_z<0.04 and, in most cases, competitive or better parameter constraints than Gaussian or top-hat bins, despite higher shot noise. The paper concludes that semi-Gaussian binning is the most suitable choice for transverse BAO analyses, particularly for low-redshift surveys.
Significance. If robust, the paper identifies a practical and often ignored issue—bin-shape-dependent projection bias in transverse BAO measurements—and proposes an easily implementable correction. The qualitative asymmetry (Gaussian underestimates, top-hat overestimates) is physically plausible, and the internal comparison across two surveys and many widths is a useful survey-design exercise. The paper does not provide code, machine-checked proofs, or a derived formula for its correction, so its contribution is primarily a forecast/caveat. However, the central claims currently rest on an inconsistent width definition, a single hand-picked semi-Gaussian shape, and a confounded FoM comparison; with these issues fixed, the paper would be a useful contribution to the BAO forecasting literature.
major comments (4)
- [§3, Eq. (3.10), Figs. 2/3] The definition of the semi-Gaussian bin is internally inconsistent. The text states σ̃_z = 0.01 for the semi-Gaussian (and σ̃_z = 1 for the top-hat), but the captions of Figures 2 and 3 specify '2σ_z = 0.033' for both the semi-Gaussian and top-hat, with the Gaussian shown as σ_z = 0.0165. The Fisher forecast in §7 later refers to σ_z = 0.016. The 'full width same' rule in §3 is not satisfied by these numbers if σ̃_z ≠ 2σ_z for the semi-Gaussian. The authors must specify the exact widths used in every figure and calculation and demonstrate that the three shapes have equal effective support, or explain why the comparison is still fair. Without this, the ranking of bin shapes in Sections 5 and 6 may be an artifact of width mismatch rather than shape.
- [§5, Eqs. (5.1)–(5.3)] The proposed correction θ_BAO = [1 − α_− − α_+] θ_fit is introduced without derivation. The α_± are defined as fractional shifts of the fiducial θ_BAO evaluated at the half-bin edges, but no argument is given for why the total bias is the sum of these two terms with equal weights, nor why a linear subtraction of this form corrects the peak location. Figures 12 and 13 show that α̃ − α is not zero and varies substantially with z_c and σ_z, yet no quantitative metric (e.g., residual RMS) or comparison to an independent estimator is provided. The correction should be derived from a model of the peak shift (e.g., a weighted average of the projection kernel) or validated on mock realizations; as it stands, Eq. (5.1) is an untested ad hoc formula.
- [§3, Eq. (3.10); §5, Figs. 10/11] The semi-Gaussian shape is specified by A=0.2, B=0.8 and a single σ̃_z, but no sensitivity scan over these parameters is presented. The central conclusion that the semi-Gaussian is the most accurate bin shape rests on this hand-picked hybrid. Figures 10 and 11 show that the semi-Gaussian α curve lies between the overestimating top-hat and the underestimating Gaussian; a different A/B choice would interpolate differently and could change the ranking. The authors should test a few values of A (e.g., 0.1, 0.3, 0.5) with B=1−A and σ̃_z fixed, and show whether the superiority for σ_z<0.04 persists. Without this, the claim is not robust.
- [§6, Figs. 14/15, Appendix B] The FoM comparison as a function of σ_z is confounded by the fact that the bin centers shift with σ_z, moving into regions of higher N(z) and reducing shot noise, as the paper itself acknowledges in §6 and Appendix B. Thus the FoM peaks at σ_z≈0.03–0.04 are driven by the survey selection function and bin placement, not by the bin shape. To claim that the semi-Gaussian improves parameter constraints, the authors should control for this: fix the bin-center positions while varying σ_z, hold the number of bins and effective volume constant, or compare at fixed shot-noise level. The '3 bins' analysis in Figures 8/9 is a step toward this, but the main σ_z-dependence plots in Figures 14/15 do not support a shape-only conclusion.
minor comments (5)
- [§3, Eq. (3.10)] The statement 'σ̃_z = 1 for the top-hat bins' is confusing; presumably this makes the exponential term negligible, giving an approximately constant window. Please clarify the top-hat limit explicitly.
- [§5, footnote] The footnote '130 bin schemes are shown in figure 17' appears as a stray, incomplete sentence; also, Figure 17 is in the appendix but the reference is unclear.
- [Figs. 2/3 captions] The captions read 'Gaussian σ_z = 0.0165, σ_z = 0.0165' and 'Semi-gaussian 2σ_z = 0.033, 2σ_z = 0.033'; this duplicated notation is confusing and should be reconciled with the σ̃_z notation used in §3.
- [Abstract and §7] The abstract claims the semi-Gaussian 'best recovers the BAO signal for σ_z<0.04', but §7 states that for DESI, semi-Gaussian and Gaussian are comparable at σ_z=0.01. Please qualify the abstract to reflect the survey-dependent nuance.
- [§4, Eq. (4.1)] The Fisher matrix expression appears to have missing summation over the i,j indices in CovM^{-1}; please clarify the indexing or define the covariance of the data vector explicitly.
Circularity Check
No significant circularity: the semi-Gaussian ranking emerges from a controlled forecast and is not imposed by construction.
full rationale
The paper's derivation chain is self-contained. The BAO peak positions are computed numerically from angular correlation functions generated through Eqs. (3.4)-(3.7) with a stated fiducial Planck cosmology and survey N(z); comparing those peaks to the fiducial θ_BAO from Eq. (3.8) is a standard recovery/forecast test, not a circular prediction. No parameter is fitted to the target θ_BAO and then renamed a prediction; the semi-Gaussian advantage is an emergent ranking across simulated bins. The adjacent-redshift correction in Eqs. (5.1)-(5.3) uses fiducial θ values to define α± and is then validated by comparing α̃ to the simulated α; this is an internal consistency check of an approximate model, not an identity. The self-citations [41] and [42] are used for context and side remarks ('the optimal redshift spacing depends on z_c, as shown in [41]') and do not carry the central claim. The paper itself acknowledges in §6 and Appendix B that FoM peaks near σ_z≈0.04 arise partly from bin centers moving into higher-N(z) regions, which weakens the parameter-constraint interpretation but is a robustness/correctness issue, not circularity. The hand-picked A=0.2/B=0.8 semi-Gaussian shape and the ambiguous width-matching rule are legitimate concerns about sensitivity, but they do not make the result equivalent to its inputs by construction.
Axiom & Free-Parameter Ledger
free parameters (2)
- semi-Gaussian shape parameters =
A=0.2, B=0.8, σ̃_z=0.01
- bin-width matching relation =
σ̃_z = 2σ_z (Gaussian σ_z half of σ̃_z)
axioms (5)
- domain assumption The angular power spectrum projection with radial selection function (Eqs. 3.4-3.5) and the Legendre transform (Eq. 3.7) capture the full BAO signal; no Limber approximation or window-function deconvolution is applied.
- domain assumption HMCode-2020 (Mead et al. 2019) provides an adequate non-linear matter power spectrum with BAO damping (Eq. 3.6).
- domain assumption The galaxy bias models for SKA (Camera et al. 2015) and DESI LRG (Ntelis et al. 2018) are representative of the final surveys.
- ad hoc to paper The correction (5.1)–(5.3) assumes the measured angular scale θ_fit differs from the true θ_BAO by an additive combination of the two half-bin fiducial fractional shifts α_±, with no weight factor.
- domain assumption Fisher matrix formalism with independent ℓ-modes and Gaussian covariance (Eqs. 4.1-4.2) is valid for the surveys and scales (20<ℓ<300).
read the original abstract
We investigate the transverse BAO projection effect caused by redshift binning uncertainty ($z_c$). For SKA HI and DESI LRG surveys, we compare Gaussian, top-hat, and semi-Gaussian bins over widths $0.01<\sigma_z<0.1$, and propose a statistical correction using adjacent redshifts. The semi-Gaussian bin best recovers the BAO signal for $\sigma_z<0.04$, despite higher shot noise. Constraints are survey-dependent: Gaussian binning is weakest for SKA, while for DESI semi-Gaussian is tightest for $\sigma_z<0.04$ (otherwise comparable). The semi-Gaussian scheme offers the optimal balance between cosmological parameter constraints and BAO fidelity, making it robust for multi-probe analyses.
Reference graph
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discussion (0)
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