Constraint on Lorentz Invariance Violation for spectral lag transition in GRB 160625B using profile likelihood

Shalini Ganguly; Shantanu Desai

REVIEW 2 major objections 5 minor 27 references

Constraint on Lorentz Invariance Violation for spectral lag transition in GRB 160625B using profile likelihood

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A profile-likelihood reanalysis of the GRB 160625B spectral-lag data finds no interior minimum for the Lorentz-invariance-violation scale below the Planck scale, yielding one-sided lower limits of $2.55\times10^{16}$ GeV and…

desk verdict Useful profile-likelihood reanalysis that likely overturns the bounded Bayesian interval for GRB 160625B, but the quoted 95% limits rest on an unvalidated Δχ²=4.0 calibration. read the letter →

arxiv 2411.09248 v2 pith:2AKLYBEV submitted 2024-11-14 astro-ph.HE astro-ph.IM

Shantanu Desai , Shalini Ganguly This is my paper · ORCID

classification astro-ph.HEastro-ph.IM

keywords Lorentzinvarianceviolationspectrallaggamma-rayburstsprofilelikelihoodquantumgravityenergyscalefrequentistinferenceGRB160625B

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 reanalyzes the spectral-lag data of gamma-ray burst GRB 160625B with a frequentist profile-likelihood method, revisiting earlier Bayesian work that reported bounded credible intervals for the Lorentz-invariance-violating energy scale $E_{QG}$. The authors find that, for both linear and quadratic models of energy-dependent photon speed, the profiled $\chi^2$ decreases monotonically as $E_{QG}$ approaches the Planck scale, so no interior minimum exists below the Planck energy. Consequently they quote one-sided 95% lower limits, $E_{QG} \geq 2.55 \times 10^{16}$ GeV for linear and $E_{QG} \geq 1.85 \times 10^{7}$ GeV for quadratic LIV, instead of central intervals. The result matters because it shows how the choice between marginalizing and profiling over astrophysical nuisance parameters can change the form of the final constraint on a fundamental physics scale.

What carries the argument

The central tool is the profile likelihood, defined by maximizing the full Gaussian likelihood over the nuisance parameters $(\tau, \alpha)$ for each fixed $E_{QG}$; in practice this is done by minimizing $\chi^2$ over $(\tau,\alpha)$ on a logarithmic grid in $E_{QG}$ with a Nelder-Mead simplex and cross-checked with Powell minimization. The resulting $\Delta\chi^2$ curve is calibrated with the standard asymptotic result that $\Delta\chi^2$ follows a $\chi^2$ distribution with one degree of freedom, and the 95% lower limit is read off where $\Delta\chi^2 = 4$, with the caveat that the boundary-corrected prescription applies near the physical boundary. The load-bearing feature is that the profile-likelihood curves are monotone decreasing, so the only extremum consistent with the data sits at the Planck-scale boundary.

What would settle it

Generate Monte Carlo realizations of the 37 spectral-lag measurements from the best-fit model with no LIV, fit each realization with the same profile-likelihood procedure, and check the coverage of the reported 95% one-sided intervals; if coverage is substantially below 95% (or if $\Delta\chi^2=4$ is not the right one-sided cutoff), the quoted limits would need revision. Equivalently, if a scan that extends the grid above the Planck scale finds an interior global minimum, the monotonicity claim would be falsified.

Watch

Extended reading notes

Core claim

Using the same data, likelihood, and parametric model as the earlier analysis (ref. [5]), the authors profile over the two astrophysical lag parameters $\tau$ and $\alpha$ and scan $E_{QG}$ on a logarithmic grid from $10^{6}$ to $10^{19}$ GeV. For both $n=1$ and $n=2$ LIV, the resulting $\Delta\chi^2(E_{QG}) = \chi^2(E_{QG}) - \chi^2_{\min}$ decreases monotonically with increasing $E_{QG}$, with the minimum attained at the upper edge of the grid, the Planck scale. Because no interior minimum exists below the Planck boundary, the paper argues that a one-sided lower limit is the correct statistical statement, and it derives 95% lower limits of $2.55 \times 10^{16}$ GeV and $1.85 \times 10^{7}$ GeV for linear and quadratic LIV, respectively, from the $\Delta\chi^2 = 4$ intercepts. This directly contrasts with the closed $1\sigma$ intervals obtained by Bayesian marginalization in refs. [5] and [7].

Load-bearing premise

The quoted limits assume that the distribution of the profile-likelihood ratio $\Delta\chi^2$ is the asymptotic one-degree-of-freedom $\chi^2$, with the 95% cutoff at $\Delta\chi^2 = 4$, even though the global minimum used to define $\Delta\chi^2$ sits at the Planck-scale boundary of the parameter space.

Editorial extensions

If this is right

If the profiling result is correct, the previously reported bounded credible intervals for $E_{QG}$ are not reproduced; the data only support a lower limit, not a finite range.
The method provides a prior-free way to set one-sided limits on $E_{QG}$, avoiding the volume effects that can arise when marginalizing over nuisance parameters.
The same procedure can be applied to other gamma-ray burst spectral-lag datasets that have been analyzed only with Bayesian methods, potentially converting bounded intervals into lower limits or vice versa.
The monotone $\Delta\chi^2$ behavior implies the GRB 160625B spectral-lag data show no statistically significant LIV-induced turnover below the Planck scale in these models.

Reading between the lines

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

A natural extension would be a Monte Carlo coverage check: simulate mock lag datasets under the null hypothesis of no LIV and see whether the $\Delta\chi^2 = 4$ cutoff really gives 95% coverage when the fitted minimum is at the boundary; if the correct one-sided threshold is instead $\Delta\chi^2 \simeq 2.71$, the quoted limits would shift by a factor related to the shape of the curve.
The contrast with Bayesian intervals may owe to the volume effect in marginalization; a direct comparison of the profile likelihood with a profile posterior could isolate whether the prior choice or the marginalization itself produces the bounded intervals.
If applied to the larger sample of GRBs with spectral-lag data, the method could test whether the monotone trend is generic, which would strengthen the case that previously reported LIV constraints from spectral lags should be re-expressed as lower limits.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

This is a solid, useful paper. The genuinely new thing is the application of profile likelihood to a GRB spectral-lag LIV analysis, and it produces a result absent from the prior Bayesian literature: the Δχ² curve for EQG decreases monotonically to the Planck scale, so there is no interior minimum, and the previous bounded 1σ intervals from Wei et al. (2017) and Gunapati et al. (2022) look like consequences of marginalization. The authors ship code and data and cross-check the minimization with two independent algorithms. That earns credit.

The main soft spot is the confidence calibration. They quote 95% c.l. lower limits from the intercept at Δχ² = 4.0, which is the 95.4% quantile of a chi-square with one dof for a two-sided likelihood-ratio test, not the standard one-sided 95% threshold of Δχ² = 2.71. Second, the minimum sits at the Planck-scale boundary, so Wilks regularity conditions are not automatically satisfied. Their note that the Δχ² = 4 intercept is far from the boundary doesn't address the fact that the reference maximum is on the boundary. Cleaner to say the limits are plausible profile-likelihood crossings; without a coverage study or Feldman-Cousins treatment, the '95%' label is not established.

This is fixable, not load-bearing. The qualitative result — monotone profile, no bounded interval — is unaffected by the threshold choice; only the numerical limits shift. The paper is clearly written, honest about assumptions, and the citation pattern is fine; self-citations are to background and their own earlier work, not circular.

I'd send this to a serious referee. The calibration point needs a careful check, but the core reanalysis is informative and the method transfer to GRB lags is new. For me it's a conditional accept with the confidence statement to be redone.

Referee Report

2 major / 5 minor

Summary. Desai and Ganguly reanalyze the GRB 160625B spectral-lag data of Wei et al. (2017) using profile likelihood. They profile over the intrinsic-lag parameters tau and alpha, scan E_QG on a logarithmic grid from 10^6 to 10^19 GeV, and find that Delta-chi^2 decreases monotonically with E_QG for both linear and quadratic LIV, with the minimum at the Planck-scale upper boundary. They therefore quote one-sided 95% lower limits E_QG >= 2.55e16 GeV (n=1) and E_QG >= 1.85e7 GeV (n=2), and argue that profile likelihood avoids the bounded Bayesian credible intervals obtained by marginalization.

Significance. If the statistical calibration is correct, this is a useful proof-of-principle: it demonstrates that the choice of marginalization versus profiling can change the qualitative form of the constraint, and it provides public code and a reproducible pipeline for GRB LIV analyses. The central qualitative result, namely the absence of an interior minimum in the profiled chi-square, is clearly presented and is robust to the minimization algorithm, since Nelder-Mead and Powell give the same result. The numeric 95% limits, however, are not yet established because the threshold and boundary treatment are not justified in the manuscript.

major comments (2)

[Section IV, Figs. 1-2] The limits are read from the Delta-chi^2 = 4.0 intercept, which the text labels '95.4% (95%, to shorten notation)'. For a one-sided 95% lower limit on one parameter, the standard likelihood-ratio threshold is Delta-chi^2 = 2.71 (the 90th percentile of chi-square with one degree of freedom), whereas Delta-chi^2 = 4.0 corresponds to a central two-sided 95.4% interval. Because the profile decreases with E_QG, the Delta-chi^2 = 4.0 intercept is larger than the Delta-chi^2 = 2.71 intercept, so the quoted limits are stronger than a conventional one-sided 95% limit. Please recompute the limits with the one-sided threshold and state explicitly which confidence convention is being used.
[Section IV] The justification for using the Neyman/Wilks calibration is that the Delta-chi^2 = 4 intercept is far from the Planck boundary, but the relevant regularity condition concerns the location of the global maximum used as the reference: here chi^2_min sits at the Planck-scale edge of the grid. The likelihood-ratio statistic is therefore not automatically asymptotically chi-square with one degree of freedom, and the Feldman-Cousins prescription or a Monte Carlo coverage check is required even when the intercept is far from the boundary. Please add a coverage check or use the Feldman-Cousins prescription before quoting the limits as 95% confidence limits.

minor comments (5)

[Sections IV and V] The GRB name is misspelled as 'GRB 1606025B' in the section headings; it should be 'GRB 160625B'.
[Section IV] 'Newman prescription' should read 'Neyman prescription'.
[Section IV] The phrase '95.4% (95%, to shorten notation)' is inaccurate; 95.4% is not a shorthand for 95%. Please use the precise percentile corresponding to the chosen confidence convention.
[Sections I and V] The comparison mixes 1-sigma Bayesian credible intervals from W17 with 95% frequentist lower limits; a sentence clarifying that these are not directly comparable confidence levels would avoid confusion.
[Section II, Eq. (3)] The cosmological parameters H0 and Omega_M are fixed to the values used by W17; the paper should state explicitly that no uncertainty from these parameters is propagated into the quoted limits.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: EQG is scanned rather than fitted, and the profile-likelihood limits are read from the resulting Δχ² curves without importing the target result as an input.

full rationale

The paper's derivation chain is self-contained with respect to the claims made. The parameter of interest, EQG, is not fitted to the data; instead, a logarithmically spaced grid in EQG is scanned, and for each grid point the nuisance parameters τ and α are profiled out by minimizing χ². The resulting Δχ²(EQG) curves are then used to read off lower limits at the Δχ² = 4 crossing. No equation defining the result is equivalent to an input by construction, and no fitted parameter is renamed as a prediction. The model and data are imported from Wei et al. (2017), but that is an external input, not a result being derived, and the paper does not claim to derive the model from first principles. The authors' self-citations [8–10] appear only as background examples of earlier Bayesian spectral-lag analyses and do not carry the central claim. The only substantive concern, namely whether the Newman/Wilks Δχ² = 4.0 calibration is valid when the global χ² minimum sits at the Planck-scale boundary, is a statistical coverage issue rather than a circularity: it questions the confidence-level calibration, not whether the quoted limit is logically presupposed by the inputs. The paper explicitly mentions Feldman-Cousins but declines to use it; this is a limitation or robustness concern, not a circular step. Overall, the analysis is a straightforward frequentist re-analysis of previously published data with the same parametric model, and its headline lower limits are genuine outputs of the profile-likelihood computation.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The analysis adds no new entities. It fits two nuisance parameters (tau, alpha) and scans EQG. The main prior input is W17's spectral-lag table and phenomenological lag model; the new statistical step is profiling out tau and alpha. The confidence calibration via Wilks and Newman is the least externally anchored ingredient.

free parameters (2)

tau (intrinsic lag normalization) = not reported
Free parameter in Eq. (2); profiled over for each EQG in the likelihood minimization.
alpha (intrinsic lag power-law index) = not reported
Free parameter in Eq. (2); profiled over for each EQG in the likelihood minimization.

assumptions (5)

domain assumption Intrinsic time lag follows a power law in energy with fixed pivot E0 = 11.34 keV (Eq. 2)
Adopted from Wei et al. 2017; if the astrophysical lag model is wrong, the EQG limits are not meaningful.
domain assumption Per-point errors are Gaussian and known (Eq. 4)
The likelihood assumes independent Gaussian errors with the published sigma_i; no validation of Gaussianity is given.
standard math Wilks theorem applies to the profile-likelihood delta-chi-squared with one degree of freedom
Used to convert delta-chi-squared = 4.0 into a 95.4% confidence threshold in Section IV; may not hold exactly when the global minimum sits at the physical boundary.
domain assumption Planck scale (10^19 GeV) is the physical upper boundary for EQG
Used as the reference chi-squared minimum for delta-chi-squared and to define one-sided limits in Section IV.
domain assumption Cosmological parameters H0 = 67.3 km/s/Mpc and Omega_M = 0.315
Fixed inputs from Wei et al. 2017 in Eq. (3); uncertainties are not propagated.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Constraint on Lorentz Invariance Violation for spectral lag transition in GRB 160625B using profile likelihood." pith.science (2026). https://pith.science/paper/2AKLYBEV

@misc{pith2026241109248,
  author       = {Pith},
  title        = {Pith review of: Constraint on Lorentz Invariance Violation for spectral lag transition in GRB 160625B using profile likelihood},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2AKLYBEV}},
  note         = {Machine review of arXiv:2411.09248}
}

abstract

We reanalyze the spectral lag data for GRB 160625B using frequentist inference in order to constrain the energy scale ($E_{QG}$) of Lorentz Invariance Violation (LIV). For this purpose, we use profile likelihood to deal with the astrophysical nuisance parameters. This is in contrast to Bayesian inference implemented in previous works, where marginalization was carried out over the nuisance parameters. We show that with profile likelihood, we do not find a global minimum for $\chi^2$ as a function of $E_{QG}$ below the Planck scale for both linear and quadratic models of LIV, whereas bounded credible intervals were previously obtained using Bayesian inference. Therefore, we can set one-sided lower limits in a straightforward manner. We find that $E_{QG} \geq 2.55 \times 10^{16}$ GeV and $E_{QG} \geq 1.85 \times 10^7$ GeV at 95\% c.l., for linear and quadratic LIV, respectively. Therefore, this is the first proof-of-principles application of profile likelihood method to the analysis of GRB spectral lag data to constrain LIV.

Figures

Figures reproduced from arXiv: 2411.09248 by the authors.

**Figure 2.** FIG. 2: ∆ [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

27 extracted references · 13 canonical work pages

[1]

Desai, in Recent Progress on Gravity Tests

S. Desai, in Recent Progress on Gravity Tests. Chal- lenges and Future Perspectives , edited by C. Bambi and A. C´ ardenas-Avenda˜ no (2024), pp. 433–463

work page 2024
[2]

Y.-W. Yu, H. Gao, F.-Y. Wang, and B.-B. Zhang, in Handbook of X-ray and Gamma-ray Astrophysics. Edited by Cosimo Bambi and Andrea Santangelo (2022), p. 31

work page 2022
[3]

Wei and X.-F

J.-J. Wei and X.-F. Wu, in Handbook of X-ray and Gamma-ray Astrophysics. Edited by Cosimo Bambi and Andrea Santangelo (2022), p. 82

work page 2022
[4]

Amelino-Camelia, J

G. Amelino-Camelia, J. Ellis, N. E. Mavromatos, D. V. Nanopoulos, and S. Sarkar, Nature (London) 393, 763 (1998), astro-ph/9712103

arXiv 1998
[5]

A New Test of Lorentz Invariance Violation: the Spectral Lag Transition of GRB 160625B

J.-J. Wei, B.-B. Zhang, L. Shao, X.-F. Wu, and P. M´ esz´ aros, Astrophys. J. Lett. 834, L13 (2017), 1612.09425

work page Pith review arXiv 2017
[6]

Statistical Significance of spectral lag transition in GRB 160625B

S. Ganguly and S. Desai, Astroparticle Physics 94, 17 (2017), 1706.01202

work page Pith review arXiv 2017
[7]

Variational Inference as an alternative to MCMC for parameter estimation and model selection

G. Gunapati, A. Jain, P. K. Srijith, and S. Desai, PASA 39, e001 (2022), 1803.06473

work page Pith review arXiv 2022
[8]

Agrawal, H

R. Agrawal, H. Singirikonda, and S. Desai, JCAP 2021, 029 (2021), 2102.11248

arXiv 2021

Show all 27 references

[9]

Desai, R

S. Desai, R. Agrawal, and H. Singirikonda, European Physical Journal C 83, 63 (2023), 2205.12780

2023 arXiv
[10]

Pasumarti and S

V. Pasumarti and S. Desai, Journal of High Energy As- trophysics 40, 41 (2023), 2307.02296

2023 arXiv
[11]

Particle Data Group, P. A. Zyla, R. M. Barnett, J. Beringer, O. Dahl, D. A. Dwyer, D. E. Groom, C. J. Lin, K. S. Lugovsky, E. Pianori, et al., Progress of Theo- retical and Experimental Physics 2020, 083C01 (2020)

2020
[12]

Herold, E

L. Herold, E. G. M. Ferreira, and E. Komatsu, Astrophys. J. Lett. 929, L16 (2022), 2112.12140

2022 arXiv
[13]

Campeti and E

P. Campeti and E. Komatsu, Astrophys. J. 941, 110 (2022), 2205.05617

2022 arXiv
[14]

E. ´O. Colg´ ain, S. Pourojaghi, and M. M. Sheikh-Jabbari, arXiv e-prints arXiv:2406.06389 (2024), 2406.06389

2024 arXiv
[15]

Karwal, Y

T. Karwal, Y. Patel, A. Bartlett, V. Poulin, T. L. Smith, and D. N. Pfeffer, arXiv e-prints arXiv:2401.14225 (2024), 2401.14225

2024 arXiv
[16]

Herold, E

L. Herold, E. G. M. Ferreira, and L. Heinrich, arXiv e- prints arXiv:2408.07700 (2024), 2408.07700

2024 arXiv
[17]

Jacob and T

U. Jacob and T. Piran, JCAP 1, 031 (2008), 0712.2170

2008 arXiv
[18]

Trotta, ArXiv e-prints (2017), 1701.01467

R. Trotta, ArXiv e-prints (2017), 1701.01467

2017 arXiv
[19]

Sharma, Annual Review of Astron

S. Sharma, Annual Review of Astron. and Astrophys. 55, 213 (2017), 1706.01629

2017 arXiv
[20]

Krishak and S

A. Krishak and S. Desai, JCAP 2020, 006 (2020), 2003.10127

2020 arXiv
[21]

S. S. Wilks, The annals of mathematical statistics 9, 60 (1938)

1938
[22]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in FORTRAN. The art of scientific computing (1992)

1992
[23]

G. J. Feldman and R. D. Cousins, Phys. Rev. D 57, 3873 (1998), physics/9711021

1998 arXiv
[24]

R. D. Cousins, American Journal of Physics 63, 398 (1995)

1995
[25]

G´ omez-Valent, Phys

A. G´ omez-Valent, Phys. Rev. D 106, 063506 (2022), 2203.16285

2022 arXiv
[26]

Kerscher and J

M. Kerscher and J. Weller, arXiv e-prints arXiv:2408.02063 (2024), 2408.02063

2024 arXiv
[27]

Raveri, C

M. Raveri, C. Doux, and S. Pandey, arXiv e-prints arXiv:2409.09101 (2024), 2409.09101

2024 arXiv

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

Desai, in Recent Progress on Gravity Tests

S. Desai, in Recent Progress on Gravity Tests. Chal- lenges and Future Perspectives , edited by C. Bambi and A. C´ ardenas-Avenda˜ no (2024), pp. 433–463

work page 2024

[2] [2]

Y.-W. Yu, H. Gao, F.-Y. Wang, and B.-B. Zhang, in Handbook of X-ray and Gamma-ray Astrophysics. Edited by Cosimo Bambi and Andrea Santangelo (2022), p. 31

work page 2022

[3] [3]

Wei and X.-F

J.-J. Wei and X.-F. Wu, in Handbook of X-ray and Gamma-ray Astrophysics. Edited by Cosimo Bambi and Andrea Santangelo (2022), p. 82

work page 2022

[4] [4]

Amelino-Camelia, J

G. Amelino-Camelia, J. Ellis, N. E. Mavromatos, D. V. Nanopoulos, and S. Sarkar, Nature (London) 393, 763 (1998), astro-ph/9712103

arXiv 1998

[5] [5]

A New Test of Lorentz Invariance Violation: the Spectral Lag Transition of GRB 160625B

J.-J. Wei, B.-B. Zhang, L. Shao, X.-F. Wu, and P. M´ esz´ aros, Astrophys. J. Lett. 834, L13 (2017), 1612.09425

work page Pith review arXiv 2017

[6] [6]

Statistical Significance of spectral lag transition in GRB 160625B

S. Ganguly and S. Desai, Astroparticle Physics 94, 17 (2017), 1706.01202

work page Pith review arXiv 2017

[7] [7]

Variational Inference as an alternative to MCMC for parameter estimation and model selection

G. Gunapati, A. Jain, P. K. Srijith, and S. Desai, PASA 39, e001 (2022), 1803.06473

work page Pith review arXiv 2022

[8] [8]

Agrawal, H

R. Agrawal, H. Singirikonda, and S. Desai, JCAP 2021, 029 (2021), 2102.11248

arXiv 2021