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arxiv: 2606.11504 · v1 · pith:WNPOAUW5new · submitted 2026-06-09 · 🌀 gr-qc · astro-ph.IM

Statistical-Uncertainty-Driven Selection of Evaluation Frequency for Time-Dependent Sensing Calibration: A Demonstration with KAGRA Data

Shingo Hido , Takahiro Yamamoto , Dan Chen , Takahiro Sawada , Shinji Miyoki This is my paper

Pith reviewed 2026-06-27 11:58 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.IM
keywords gravitational wave calibrationsensing functionstatistical uncertaintyevaluation frequency selectionKAGRAtime-dependent calibrationamplitude and phase intervals
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The pith

A statistical method selects 244 Hz to minimize calibration uncertainty in KAGRA sensing data

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

The paper introduces a framework for choosing evaluation frequencies to track slow changes in a gravitational-wave detector's sensing response when hardware constraints block the most precise frequencies. Using KAGRA data from the start of the O4 run, where the practical calibration line sits at 32.7 Hz while the cavity pole is near 18 Hz, the approach builds the sensing function for each candidate frequency and measures segment-wise uncertainty via empirical percentiles of the observed distribution. Candidates are ranked by a score that balances amplitude and phase interval widths. With equal weighting of a 1 percent amplitude width and a 1 degree phase width, 244 Hz is chosen in every 4096-second segment. Relative to the reference, this choice shrinks the amplitude interval width to roughly one quarter over a broad range while phase widths stay comparable.

Core claim

When a 1% amplitude interval width and a 1 degree phase interval width are weighted equally, 244 Hz is selected in all 4096 s analysis segments throughout the analyzed period. Relative to the reference frequency of 32.7 Hz, the amplitude interval width is reduced to about one quarter over a broad frequency range, while the phase interval width remains broadly comparable.

What carries the argument

A ranking score that combines the widths of amplitude and phase uncertainty intervals, where the uncertainties are obtained from empirical percentiles of the sample distribution in each analysis segment.

If this is right

  • The selected frequency can replace or supplement the reference line for tracking sensing variations in ongoing runs.
  • The separate assessment of frequency-translation discrepancy provides a way to correct for any offset introduced by moving the evaluation point.
  • The same percentile-based scoring can be applied to other detectors that face injection-frequency constraints.
  • Segment-by-segment re-ranking allows the chosen frequency to adapt if data properties change over longer periods.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The percentile method could be tested against bootstrap or analytic variance estimates to check robustness when sample sizes vary.
  • Integrating the ranking into automated calibration pipelines would allow dynamic frequency choice without manual intervention.
  • The framework may generalize to other time-varying transfer functions in precision instruments where direct measurement at optimal points is blocked.

Load-bearing premise

The segment-wise statistical uncertainty is quantified from empirical percentiles of the sample distribution and that this measure accurately reflects the true variability in the sensing function parameters without unaccounted biases from data properties or model assumptions.

What would settle it

An independent end-to-end simulation or separate calibration measurement that injects known signals and directly compares the recovered sensing parameters at 244 Hz versus 32.7 Hz; if the actual errors at 244 Hz are not smaller by the predicted factor, the selection is falsified.

Figures

Figures reproduced from arXiv: 2606.11504 by Dan Chen, Shingo Hido, Shinji Miyoki, Takahiro Sawada, Takahiro Yamamoto.

Figure 1
Figure 1. Figure 1: Representative heatmap of the normalized score [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Histogram of the relative score difference between the best candidate at 244 Hz and the [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: O4a-wide summary of the 68% interval widths of the sample distribution for the amplitude and phase of the sensing function, evaluated at 244 Hz for all 4096 s segments. The horizontal axis denotes the frequency f. At each frequency, the median and the 16th–84th percentiles over segments are shown relative to the reference-frequency result at 32.7 Hz. The phase interval width remains broadly unchanged, whil… view at source ↗
Figure 4
Figure 4. Figure 4: O4a-wide summary of the discrepancy between the reference-frequency result at [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Representative comparison of the sensing function in a single [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the normalized 68% interval widths of the statistical uncertainty for the sensing function, evaluated at 244 Hz and 468 Hz and shown relative to the reference-frequency result at 32.7 Hz. The upper and lower panels show the amplitude and phase results, respectively. While 468 Hz yields a smaller amplitude interval width than 244 Hz over much of the frequency range, it also leads to a substant… view at source ↗
read the original abstract

Accurate calibration of the gravitational-wave strain h(t) is essential for both detection and astrophysical inference. In operating detectors, slow temporal variations in the sensing response are tracked using calibration lines, but practical constraints can prevent those lines from being injected at frequencies that are favorable for precise estimation of sensing-side parameters. We present a statistical framework for preselecting evaluation frequencies under such constraints. We apply this framework to KAGRA data from the first part of the fourth LIGO-Virgo-KAGRA Observing Run, for which the nominal cavity-pole frequency was about 18 Hz, while the sensing-side calibration line used in practice was injected at 32.7 Hz. For each candidate evaluation frequency, we construct the sensing function, quantify its segment-wise statistical uncertainty from empirical percentiles of the sample distribution, and rank the candidates using a score that combines the interval widths of the amplitude and phase. When a 1% amplitude interval width and a 1 degree phase interval width are weighted equally, 244 Hz is selected in all 4096 s analysis segments throughout the analyzed period. Relative to the reference frequency of 32.7 Hz, the amplitude interval width is reduced to about one quarter over a broad frequency range, while the phase interval width remains broadly comparable. We also assess the discrepancy introduced by frequency translation separately. These results suggest that the proposed method provides a useful statistical preselection framework for evaluation frequencies under practical operational constraints.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a statistical framework for preselecting evaluation frequencies for time-dependent sensing calibration in gravitational-wave detectors under operational constraints. Applied to KAGRA O4 data (nominal cavity pole ~18 Hz, reference line at 32.7 Hz), it constructs the sensing function at candidate frequencies, quantifies segment-wise statistical uncertainty via empirical percentiles of the sample distribution for amplitude and phase, and ranks candidates by a combined score. When 1% amplitude and 1° phase interval widths are weighted equally, 244 Hz is selected in every 4096 s segment; relative to 32.7 Hz the amplitude width is reduced by a factor of ~4 over a broad range while phase width remains comparable. Frequency-translation discrepancy is assessed separately.

Significance. If the percentile-based uncertainties prove reliable, the framework offers a practical, data-driven tool for optimizing calibration-line placement, which could tighten strain calibration and thereby improve both detection statistics and astrophysical inference in operating detectors.

major comments (2)
  1. [Statistical uncertainty quantification and results sections] The central claim (consistent selection of 244 Hz and factor-of-four amplitude improvement) rests on the premise that segment-wise empirical percentiles accurately capture true parameter variability. The manuscript assesses frequency-translation discrepancy separately but does not appear to include direct tests (e.g., injection-recovery simulations or comparison against known stationary segments) for systematic offsets arising from non-stationary noise, finite-sample effects, or sensing-function model assumptions; this validation gap is load-bearing for the reliability of the ranking.
  2. [Results on frequency selection] The statement that 244 Hz is selected “in all 4096 s analysis segments throughout the analyzed period” is presented without reporting the total number of segments, the distribution of scores across segments, or any measure of consistency (e.g., fraction of segments or variance of the selected frequency); this weakens the strength of the “all segments” claim.
minor comments (2)
  1. [Abstract and methods] The specific numerical thresholds (1 % amplitude, 1° phase) used for equal weighting are stated but lack an explicit justification or sensitivity study showing how the selected frequency changes with modest variations in these values.
  2. [Introduction] The relevance of the nominal cavity-pole frequency (~18 Hz) to the sensing-function construction and to the choice of candidate evaluation frequencies could be stated more explicitly for readers outside the KAGRA collaboration.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review. We address each major comment below and indicate the revisions that will be made to the manuscript.

read point-by-point responses

  1. Referee: [Statistical uncertainty quantification and results sections] The central claim (consistent selection of 244 Hz and factor-of-four amplitude improvement) rests on the premise that segment-wise empirical percentiles accurately capture true parameter variability. The manuscript assesses frequency-translation discrepancy separately but does not appear to include direct tests (e.g., injection-recovery simulations or comparison against known stationary segments) for systematic offsets arising from non-stationary noise, finite-sample effects, or sensing-function model assumptions; this validation gap is load-bearing for the reliability of the ranking.

    Authors: The empirical-percentile method is deliberately non-parametric and extracts uncertainty directly from the observed sample distribution within each data segment, thereby incorporating the effects of any non-stationarities that are actually present. The separate frequency-translation assessment already quantifies one class of model-related discrepancy. We nevertheless agree that explicit cross-checks against stationary segments or injection-recovery tests would further support the reliability of the ranking. In the revised manuscript we will add a dedicated validation subsection that performs such checks on the available KAGRA segments and discusses the remaining limitations. revision: yes

  2. Referee: [Results on frequency selection] The statement that 244 Hz is selected “in all 4096 s analysis segments throughout the analyzed period” is presented without reporting the total number of segments, the distribution of scores across segments, or any measure of consistency (e.g., fraction of segments or variance of the selected frequency); this weakens the strength of the “all segments” claim.

    Authors: We agree that the consistency claim should be quantified. The revised manuscript will state the exact number of 4096 s segments analyzed, report summary statistics (mean, median, and standard deviation) of the combined scores across those segments, and explicitly give the fraction of segments in which 244 Hz received the highest score. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical percentile ranking is self-contained data processing

full rationale

The paper's core procedure constructs the sensing function per segment, extracts amplitude and phase interval widths directly from empirical percentiles of the observed sample distribution, and ranks candidate frequencies by a weighted score on those widths. No parameter is fitted to a subset and then re-predicted; no self-citation supplies a uniqueness theorem or ansatz; the selection of 244 Hz follows immediately from applying the percentile-derived widths to the KAGRA data segments. The method therefore reduces to straightforward statistical summarization of the input time series rather than any definitional or fitted-input loop.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Ledger extracted from abstract only; full paper may contain additional parameters or assumptions not visible here.

free parameters (1)
  • relative weighting of amplitude and phase interval widths
    Example uses equal weighting of 1% amplitude and 1 degree phase; this choice affects the final ranking score.
axioms (1)
  • domain assumption Empirical percentiles of the sample distribution provide an accurate quantification of statistical uncertainty in the sensing function parameters.
    Invoked when constructing segment-wise uncertainty for each candidate frequency.

pith-pipeline@v0.9.1-grok · 5813 in / 1182 out tokens · 26548 ms · 2026-06-27T11:58:17.441923+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

14 extracted references · 10 canonical work pages

  1. [1]

    Effect of calibration errors on Bayesian parameter estimation for gravitational wave signals from inspiral binary systems in the advanced detectors era

    Salvatore Vitale et al. “Effect of calibration errors on Bayesian parameter estimation for gravitational wave signals from inspiral binary systems in the advanced detectors era”. In: Phys. Rev. D85 (6 Mar. 2012), p. 064034.url:https://link.aps.org/doi/10.1103/ PhysRevD.85.064034

    2012

  2. [2]

    Impact of calibration uncertainties on Hubble constant measurements from gravitational-wave sources

    Yiwen Huang et al. “Impact of calibration uncertainties on Hubble constant measurements from gravitational-wave sources”. In:Phys. Rev. D111 (6 Mar. 2025), p. 063034.url: https://link.aps.org/doi/10.1103/PhysRevD.111.063034

    work page doi:10.1103/physrevd.111.063034 2025

  3. [3]

    Systematic calibration error requirements for gravitational-wave detec- tors via the Cramér–Rao bound

    Evan D Hall et al. “Systematic calibration error requirements for gravitational-wave detec- tors via the Cramér–Rao bound”. In:Classical and Quantum Gravity36.20 (Sept. 2019), p. 205006.url:https://doi.org/10.1088/1361-6382/ab368c. 10

    work page doi:10.1088/1361-6382/ab368c 2019

  4. [4]

    Overview of KAGRA: Detector design and construction history

    T Akutsu et al. “Overview of KAGRA: Detector design and construction history”. In: Progress of Theoretical and Experimental Physics2021.5 (Aug. 2020), 05A101.issn: 2050- 3911.url:https://doi.org/10.1093/ptep/ptaa125

    work page doi:10.1093/ptep/ptaa125 2020

  5. [5]

    P., et al

    The LIGO Scientific Collaboration et al. “Advanced LIGO”. In:Classical and Quantum Gravity32.7 (Mar. 2015), p. 074001.url:https://doi.org/10.1088/0264-9381/32/7/ 074001

    work page doi:10.1088/0264-9381/32/7/ 2015

  6. [6]

    Advanced Virgo: a second-generation interferometric gravitational wave detector

    F Acernese et al. “Advanced Virgo: a second-generation interferometric gravitational wave detector”. In:Classical and Quantum Gravity32.2 (Dec. 2014), p. 024001.url:https: //doi.org/10.1088/0264-9381/32/2/024001

    work page doi:10.1088/0264-9381/32/2/024001 2014

  7. [7]

    GWTC-4.0: An Introduction to Version 4.0 of the Gravitational-Wave Transient Catalog

    A. G. Abac et al. “GWTC-4.0: An Introduction to Version 4.0 of the Gravitational-Wave Transient Catalog”. In:The Astrophysical Journal Letters995.1 (Dec. 2025), p. L18.url: https://doi.org/10.3847/2041-8213/ae0c06

    work page doi:10.3847/2041-8213/ae0c06 2025

  8. [8]

    Improving LIGO calibration accuracy by tracking and compensat- ing for slow temporal variations

    D Tuyenbayev et al. “Improving LIGO calibration accuracy by tracking and compensat- ing for slow temporal variations”. In:Classical and Quantum Gravity34.1 (Dec. 2016), p. 015002.url:https://doi.org/10.1088/0264-9381/34/1/015002

    work page doi:10.1088/0264-9381/34/1/015002 2016

  9. [9]

    Improving LIGO calibration accuracy by using time-dependent filters to compensate for temporal variations

    M Wade et al. “Improving LIGO calibration accuracy by using time-dependent filters to compensate for temporal variations”. In:Classical and Quantum Gravity40.3 (Jan. 2023), p. 035001.url:https://doi.org/10.1088/1361-6382/acabf6

    work page doi:10.1088/1361-6382/acabf6 2023

  10. [10]

    (Accessed: 2026- 04-27)

    Yamamoto Takahiro.Candidate of new frequencies for calibration lines. (Accessed: 2026- 04-27). 2023.url:https://klog.icrr.u-tokyo.ac.jp/osl/?r=25235

    2026

  11. [11]

    Reconstructing the calibrated strain signal in the Advanced LIGO de- tectors

    A D Viets et al. “Reconstructing the calibrated strain signal in the Advanced LIGO de- tectors”. In:Classical and Quantum Gravity35.9 (Apr. 2018), p. 095015.url:https : //doi.org/10.1088/1361-6382/aab658

    work page doi:10.1088/1361-6382/aab658 2018

  12. [12]

    Overview of KAGRA: Calibration, detector characterization, physical environmental monitors, and the geophysics interferometer

    T Akutsu et al. “Overview of KAGRA: Calibration, detector characterization, physical environmental monitors, and the geophysics interferometer”. In:Progress of Theoretical and Experimental Physics2021.5 (Feb. 2021), 05A102.issn: 2050-3911.url:https:// doi.org/10.1093/ptep/ptab018

    work page doi:10.1093/ptep/ptab018 2021

  13. [13]

    2026.url:https://arxiv.org/abs/ 2606.09010

    Shingo Hido et al.Statistical Estimation and Correction of Model-Measurement Bias in Time-Dependent Correction Factors of KAGRA. 2026.url:https://arxiv.org/abs/ 2606.09010

    Pith/arXiv arXiv 2026

  14. [14]

    (Accessed: 2026-04-01)

    Hido Shingo and Yamamoto Takahiro.MN stage in the offline/low-latency reconstruction pipelines. (Accessed: 2026-04-01). 2024.url:https://klog.icrr.u-tokyo.ac.jp/osl/ ?r=29691. 11

    2026