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Quantifying the detection likelihood of faint peaks in interferometric data through jackknifing: Test application on finding $z>10$ galaxy candidates

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper argues that the 3–5σ emission-line detections previously reported for three z>10 galaxy candidates in archival ALMA data are statistically consistent with noise, and presents a jackknife-based likelihood-ratio tool for…

desk verdict Useful jackknife tool and a plausible null result for z>10 candidates, but the headline claim overreaches because the null analysis never uses the imaging under which the original detections were claimed. read the letter →

arxiv 2501.03150 v1 pith:OHNM6HM2 submitted 2025-01-06 astro-ph.GA astro-ph.IM

Joshiwa van Marrewijk , Melanie Kaasinen , Gergö Popping , Luca Di Mascolo , Tony Mroczkowski , Leindert Boogaard , Francesco Valentino , Tom Bakx
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Ilsang Yoon
This is my paper · ORCID
classification astro-ph.GAastro-ph.IM
keywords jackknifinginterferometricdataemission-linedetectionhigh-redshiftgalaxiesfalse-positivedetectionslikelihoodratioALMAnoisecharacterization
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 argues that the tentative emission-line detections reported for three z>10 galaxy candidates in archival ALMA data are consistent with noise. The authors introduce a tool, jackknify, that randomly multiplies half of a visibility set's real and imaginary amplitudes by -1 and re-images the data, producing many noise-only realizations of the exact same measurement set. Running the same line-finder on the real cube and on 50 jackknife noise cubes yields a likelihood ratio Λ(γ) between detection and false-detection probability. For a 4σ threshold, the ratios are 0.80, 1.4, and 1.4 for GLASS-z12, GLASS-z10, and S5-z17-1, all below the paper's k=3 detection threshold, so none of the previously reported lines can be distinguished from noise.

What carries the argument

The central mechanism is jackknifing in the visibility plane: randomly multiplying half of a measurement set's real and imaginary visibility amplitudes by -1, then re-imaging, so that the coherent source signal averages to zero while the zero-mean Gaussian noise remains. This yields observation-specific noise-only cubes with the same uv-coverage, beam, and imaging-related correlated noise as the real data, from which the false-detection probability distribution PFD(x) is sampled without assuming an analytic noise model. The detection statistic is the likelihood ratio Λ(γ) = LD(γ)/LFD(γ), computed by applying the line-finding algorithm used in the paper to both the real cube and 50 jackknife realizations; the ratio exceeds the threshold k=3 when the data contain more peaks at a given S/N than the noise alone would produce.

What would settle it

Re-image the GLASS-z12 measurement set with the same tapered weighting and 150 km/s channels used in the original 5.8σ report and run the jackknife likelihood ratio; if the peak at the reported position then yields Λ ≥ 3, the conclusion that the detection is pure noise would be refuted.

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Extended reading notes

Core claim

The paper's central claim is that the previously reported 3–5σ [O III] 88 μm detections in the archival ALMA scans of GLASS-z12, GLASS-z10, and S5-z17-1 are statistically indistinguishable from the noise in those same measurement sets. The evidence is a likelihood-ratio test built from jackknife noise cubes: flipping the sign of half the complex visibilities before re-imaging removes the source while preserving the uv-coverage, beam, and correlated noise pattern, so the false-detection distribution PFD(x) is sampled directly from the data. Integrating the peak S/N distributions above γ = 4σ gives false-detection likelihoods LFD = 0.0011, 0.0054, and 0.0032; multiplied by the number of peaks in each real cube, these predict 1.3±1.1, 1.5±1.2, and 0.7±0.8 noise peaks above 4σ, and the data contain 1, 2, and 1 such peaks, giving Λ = 0.80, 1.4, and 1.4. Since Λ is below the k=3 threshold, the null hypothesis (no line) cannot be rejected for any source. The paper further shows that a JWST/MRS redshift prior for GLASS-z12 narrows the search but still leaves Λ = 1.64 at 2.5σ, below the threshold.

Load-bearing premise

Jackknife noise cubes share the exact statistical distribution of the true noise in the real data — same covariance, no leftover source signal — a premise validated only on narrow-band six-channel simulations with a simple point source and a negligible w-term.

Editorial extensions

If this is right

  • The three tentative z>10 [O III] detections (GLASS-z12, GLASS-z10, S5-z17-1) are statistically consistent with noise, with likelihood ratios 0.80, 1.4, and 1.4 at 4σ, all below the k=3 detection threshold.
  • In a blind search across ~30 GHz of ALMA bandwidth, a 4σ peak is not rare: given the ~200–1000 peaks in these cubes, ~3±2 noise peaks at S/N 4–5 are expected, so a >5σ threshold is required for secure line confirmation.
  • Even adding a JWST redshift prior for GLASS-z12 leaves the likelihood ratio at 1.64 (below k=3), so the prior does not rescue the marginal detection.
  • Detecting two lines at a matching redshift would strengthen the case, but the chance that two noise features appear at the right spatial and frequency offset must still be counted.
  • The publicly released jackknify tool can be applied to any interferometric measurement set in the standard radio-astronomy format, making the false-detection likelihood calculation reproducible for other targets.

Reading between the lines

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

  • If jackknife noise realizations remain faithful for full 30 GHz scans with continuum subtraction and multiple lines, the Λ > 3 threshold could become a standard, observation-specific detection criterion for ALMA line searches, replacing global S/N cutoffs.
  • The same visibility-differencing idea could be ported to single-dish time-domain data, as the paper hints, giving false-positive rates for future large-aperture submillimeter surveys where the beam and noise correlations differ.
  • A direct test of the method's generality would be to run jackknify on a cube with a known faint line embedded in a full-band scan and measure how often Λ exceeds 3 as a function of line S/N; the paper only validates the noise statistics, not the detection completeness across the full bandwidth.
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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 / 4 minor

Summary. The manuscript presents 'jackknify', a tool that generates noise realizations from interferometric visibilities by randomly sign-flipping half of the real and imaginary visibility amplitudes and re-imaging. The authors apply FindClump to the real data cube and to 50 jackknife realizations of three archival ALMA spectral scans targeting z>10 candidates (GLASS-z12, GLASS-z10, and S5-z17-1), compute likelihood ratios between the positive-peak distribution in the data and that in the jackknife noise, and conclude that the previously reported tentative [O III] 88 micron detections are consistent with noise. They validate the method against simobserve simulations for a six-channel point-source setup and demonstrate a Bayesian extension that incorporates a JWST redshift prior for GLASS-z12. The paper also provides a public implementation of the tool.

Significance. The tool addresses a real and timely problem: false-positive emission-line detections in broad ALMA spectral scans can bias number counts and redshift distributions of high-redshift galaxies. The strengths of the paper are the public implementation of the method, the simulation-based validation of the jackknife noise model for point sources, and the explicit quantitative comparison of expected and observed numbers of peaks above 4 sigma (1.3 vs 1, 1.5 vs 2, and 0.7 vs 1 in Table 2). If the results are interpreted as conditional on the adopted imaging, they support the null conclusion for those specific cubes. The main weakness is that the null analysis is carried out in natural-weighted, 46 km/s channel cubes, whereas the original reported detections were made with tapered, wider-channel imaging; the paper itself documents that this imaging change reduces the GLASS-z12 feature from 5.8 sigma to 2.9 sigma and the S5-z17-1 feature from 5.1 sigma to 3.9 sigma. The claim that the previously reported detections are consistent with noise is therefore not fully established for the imaging in which those detections were originally reported.

major comments (3)
  1. [Section 5.2, Table 2] The conclusion that the previously reported tentative detections are consistent with noise is computed only for the authors' fixed imaging choice (natural weighting, ~46 km/s channels). Under this imaging, the GLASS-z12 feature drops from 5.8 sigma at 400 km/s to 2.9 sigma at 280 km/s, and the S5-z17-1 feature drops from 5.1 sigma to 3.9 sigma; the authors explicitly attribute this to imaging differences and state that this 'highlights the importance of imaging the jackknifed data in the same way as the real data.' Because the likelihood ratios and false-detection probabilities in Table 2 are not computed for the tapered, wider-channel cubes in which the detections were originally reported, the central claim overreaches. The authors should either repeat the jackknifing analysis for the original imaging setups or explicitly restrict the conclusion to their adopted imaging.
  2. [Section 4, footnote 3] The simobserve validation covers only a six-channel, 31 MHz setup with a single unresolved source observed with natural weighting and under the assumption that the w-term is negligible. The three real data sets are full ~30 GHz spectral scans with continuum subtraction and multiple tunings; the paper does not validate that jackknifed realizations from such scans have the same noise distribution as the true noise, particularly regarding spectral correlations across tunings and possible residual continuum-subtraction artifacts. This is a load-bearing assumption for the method's application to the full spectral scans, and it should be either validated with a more representative simulation or clearly flagged as a scope limitation.
  3. [Section 3.2, Eq. (2)] The definition of the likelihood ratio in Eq. (2) is internally inconsistent with its use in Section 5.2 and Table 2. Equation (2) writes Lambda = Npos/Nneg and identifies negative peaks in the real cube with the false-detection distribution, while the actual analysis uses positive peaks in jackknife cubes for PFD and computes Lambda as the ratio of the number of real peaks above gamma to the expected number of jackknife peaks above gamma (approximately Nfound/(LFD x Npeaks)). Please define Lambda unambiguously and align the equation with the procedure actually implemented.
minor comments (4)
  1. [Keywords] The keyword 'galaxies:high-redsfhits' contains a typo and should be 'galaxies:high-redshift.'
  2. [Section 5.2] The text states Npeaks = 1150 for GLASS-z12 while Table 2 reports Npeaks found above 4 sigma as 1; please clarify that Npeaks is the total number of FindClump peaks in the full cube, not the number above the detection threshold.
  3. [Section 5.3] In the Bayesian subsection, the posterior is normalized and priors are introduced, but the reported value Lambda(gamma = 2.5) = 1.64 appears to be computed without explicitly showing how the JWST redshift prior enters the likelihood-ratio calculation; please clarify whether the prior is included in the quoted ratio.
  4. [Table 1 and Section 5.3] The ALMA project code for the Bakx data is written as 2021.A.00020.S in Table 1 and as 2021.A0020.S in Section 5.3; please use a consistent notation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the jackknife noise model is validated against external simobserve simulations, and the likelihood-ratio test is applied symmetrically to real and noise cubes rather than fitted to the null result.

full rationale

The derivation chain is self-contained. Jackknife noise realizations are produced by randomly sign-flipping half the visibilities and re-imaging, and the validity of this procedure is checked against external CASA simobserve simulations (Section 4, Figs. 5–6), not against the three science targets. The likelihood ratio Lambda = LD/LFD is defined from two empirically sampled peak distributions, one from the real cube and one from jackknifed noise cubes; it is not fitted to reproduce the null result. The thresholds gamma = 4 and k = 3 are fixed a priori and applied symmetrically to both distributions. The redshift-prior re-analysis of GLASS-z12 uses independent JWST/MRS data (Zavala et al. 2024b). The only self-reference is building on the visibility-differencing idea of Kaasinen et al. (2023), but the present paper independently validates the approach with simulations and releases a public tool, so the citation is not load-bearing. The dependence of the null result on the chosen imaging (natural weighting and 46 km/s channels versus the tapered, wider-channel cubes of the original reports) is a scope and generality limitation, not a circular reduction: the paper explicitly identifies the S/N difference and does not claim the conclusion is imaging-independent. No equation reduces to its own input, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The analysis introduces no new physical entities. It relies on standard radio-interferometry assumptions about Gaussian visibility noise, on the empirical validity of jackknifing as a noise estimator, and on a set of hand-chosen analysis thresholds. The free parameters are analysis choices, not fitted physical constants, and they do not determine the null result by construction.

free parameters (6)
  • Detection threshold gamma = 4 sigma (2.5 sigma in the Bayesian section)
    Chosen in Section 5.1 for the likelihood ratio calculations; gamma = 2.5 is used in the redshift-prior analysis.
  • Likelihood-ratio threshold k = 3
    Chosen in Section 5.1 to declare a detection significant, based on a 2-sigma Poisson excess.
  • Aperture radius = 0.6 arcsec
    Chosen in Section 5.1 to include the previously reported 0.5 arcsec offset detection while excluding interlopers.
  • Line-width search range = 100 to 500 km/s
    FindClump configuration in Section 5.1; affects which peaks are counted in both real and noise cubes.
  • Number of jackknife realizations = 50
    Set in Section 3.2.2 after convergence tests shown in Figure 2.
  • SExtractor detection and analysis thresholds = 2
    Modified defaults in Section 5.1 to detect low S/N clumps.
assumptions (4)
  • domain assumption Visibility-plane noise is Gaussian, additive, and zero-mean after proper calibration
    Section 3.1 states this as the basis for jackknifing, citing Thompson et al. 2017. Footnote 4 notes this breaks with calibration errors.
  • domain assumption Random sign-flipping of visibilities removes the source while preserving the noise distribution
    Section 3.1 and Section 4 validate this on simobserve simulations, but the paper notes it is not tested on wide-field or bright extended emission data.
  • domain assumption The peak distribution sampled by FindClump in jackknife cubes is an unbiased estimator of the false detection PDF
    Section 3.2.2 and Section 5.1 rely on this assumption, which depends on the chosen line-finder settings and cropping parameters.
  • domain assumption The w-term can be neglected for these small fields
    Footnote 3 states that the tools are validated only on data where the w-term was neglected.

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Cite this review

Pith. "Pith review of Quantifying the detection likelihood of faint peaks in interferometric data through jackknifing: Test application on finding $z>10$ galaxy candidates." pith.science (2026). https://pith.science/paper/OHNM6HM2

@misc{pith2026250103150,
  author       = {Pith},
  title        = {Pith review of: Quantifying the detection likelihood of faint peaks in interferometric data through jackknifing: Test application on finding $z>10$ galaxy candidates},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OHNM6HM2}},
  note         = {Machine review of arXiv:2501.03150}
}
abstract

False-positive emission-line detections bias our understanding of astronomical sources; for example, falsely identifying $z\sim3-4$ passive galaxies as $z>10$ galaxies leads to incorrect number counts and flawed tests of cosmology. In this work, we provide a novel but simple tool to better quantify the detection of faint lines in interferometric data sets and properly characterize the underlying noise distribution. We demonstrate the method on three sets of archival observations of $z>10$ galaxy candidates, taken with the Atacama Large Millimeter/Submillimeter Array (ALMA). By jackknifing the visibilities using our tool, $jackknify$, we create observation-specific noise realizations of the interferometric measurement set. We apply a line-finding algorithm to both the noise cubes and the real data and determine the likelihood that any given positive peak is a real signal by taking the ratio of the two sampled probability distributions. We show that the previously reported, tentative emission-line detections of these $z>10$ galaxy candidates are consistent with noise. We further expand upon the technique and demonstrate how to properly incorporate prior information on the redshift of the candidate from auxiliary data, such as from JWST. Our work highlights the need to achieve a significance of $\gtrsim 5\sigma$ to confirm an emission line when searching in broad 30 GHz bandwidths. Using our publicly available method enables the quantification of false detection likelihoods, which are crucial for accurately interpreting line detections.

Figures

Figures reproduced from arXiv: 2501.03150 by the authors.

Figure 1
Figure 1. Schematic of the detection inference. Given the data, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. How an increasing number of jackknife realizations leads [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Sampled noise distributions, PFD(x), as a function of the peak S/N. The gray hatched histogram shows the results from sampling the number of negative peak values of the original data set (shown with corresponding Poisson uncertainty). The blue￾filled region represents the 95% confidence interval of the posi￾tive peak values from the jackknife observations. As shown in Figures 2 & 3, jackknifing allows for a more com… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Moment-0 maps of simulated ALMA data, generated using [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Comparison of the standard deviation σmap measured from different simobserve realizations using 200 different ran￾dom seeds (orange points and corresponding histogram) and the σmap of the jackknifing for each corresponding mock observa￾tion (shaded blue squares). The t…
Figure 7
Figure 7. Figure 7: Output of the line finding done on the simulated ALMA [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: Probability distribution of false detections, [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: Posterior distribution of peaks above S/N > 2.5 and within 0′′ .6 of the JWST derived centroid as a function of fre￾quency for both the real and jackknifed realization. The Gaus￾sian prior derived from JWST/MRS Hα observation of Zavala et al. (2024b) is shown as the gr…
Figure 10
Figure 10. Figure 10: Moment-0 maps centered at ν = 254.35 GHz with a linewidth of 280 km s−1 for the real data set and three jackknife realizations which are imaged identically. In the lower left, we show the beam size. The size of the images is 1′′ .7 by 1′′ .7. The contours are drawn at…

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Reviewed August 10, 2026 · model on record in the stance chip above.