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REVIEW 3 major objections 3 minor 25 references

Bayesian model comparison of combined ANAIS-112 and COSINE-100 data finds no meaningful evidence for an annual modulation from dark-matter interactions, with log Bayes factors not exceeding 1.19.

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2026-08-03 13:41 UTC pith:HRKWZSDV

load-bearing objection Small Bayesian follow-up with a real phase-sign bug in two of its four rows; the uniform-phase rows still support no modulation. the 3 major comments →

arxiv 2512.23191 v2 pith:HRKWZSDV submitted 2025-12-29 hep-ex astro-ph.IM

Search for Annual Modulation in Combined ANAIS 112 and COSINE 100 Data using Bayesian Model Comparison

Om Godse , Shantanu Desai This is my paper
classification hep-ex astro-ph.IM
keywords annual modulationdark matter direct detectionBayesian model comparisonBayes factorCOSINE-100ANAIS-112sodium iodide detectorsDAMA anomaly
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper asks whether three years of combined data from two sodium-iodide dark-matter detectors (ANAIS-112 and COSINE-100) contain any annual modulation of the kind expected from dark-matter scattering, and answers with a Bayesian model comparison between a cosine-signal model and a constant-background model. For four different choices of priors, in both the 1-6 keV and 2-6 keV energy ranges, the natural-log Bayes factor favoring the cosine model never exceeds 1.19 (and is usually below 1.15), which the authors classify as 'barely worth mentioning' on Jeffreys' scale. The paper concludes that the combined data show no evidence for an annual cosine signal from dark-matter interactions, consistent with the frequentist analysis of the same dataset. A reader should care because this is an independent statistical check on the long-standing claim that sodium-iodide detectors see a modulated dark-matter signal; if the Bayes-factor result holds, it strengthens the case that the claimed modulation is not reproduced by two similar detectors using the same target material.

Core claim

The central claim is that Bayesian evidence does not favor an annually modulating cosine term over a constant background in the combined ANAIS-112/COSINE-100 residuals. The paper computes the natural-log Bayes factor B21 for the cosine model (M2) against the constant model (M1) for four prior configurations: uniform or DAMA-derived Gaussian priors on angular frequency and phase. In the 1-6 keV and 2-6 keV intervals, the largest ln B21 is 1.19, which Jeffreys' scale calls 'barely worth mentioning.' The authors therefore conclude that the combined three-year dataset, with 485 kg-year of exposure, provides no evidence for the annual modulation expected from dark-matter interactions.

What carries the argument

The key object is the Bayes factor B21, the ratio of marginal likelihoods of the cosine model and the constant model, computed by integrating each model's likelihood over its parameters with nested sampling. The cosine model is R(t)=S_m cos(ω(t+t0)) with amplitude, angular frequency, and phase free; the constant model is a flat rate A. Prior sets vary: uniform amplitude, uniform or Gaussian (DAMA-based) frequency, and uniform or Gaussian phase. The comparison quantifies whether the extra complexity of a yearly cosine is justified by the data.

Load-bearing premise

The load-bearing premise is that the two DAMA-based Gaussian phase priors actually center on the same phase as the DAMA claim once the model's sign convention for the cosine argument is accounted for; if that phase is misaligned, those two of four Bayes factors do not test the DAMA-preferred phase.

What would settle it

Recompute the two DAMA-normal-prior rows with the phase prior recentered on the equivalent DAMA phase under the ω(t+t0) convention (roughly day 220 rather than 145) and check whether any log Bayes factor rises above 1.15; if it does, the blanket conclusion of no evidence would need qualification.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If correct, the combined first-three-year NaI data do not support the DAMA-like annual modulation hypothesis.
  • The Bayesian conclusion matches the frequentist regression results from the same dataset, providing cross-method agreement.
  • The result holds under both uniform and DAMA-informed priors, so it is not an artifact of one particular prior choice within the ranges considered.
  • The maximum log Bayes factor of about 1.2 implies that even if a modulation exists, it is too weak to be distinguished from background in this exposure.
  • The public analysis codes allow others to extend the comparison to longer exposures as more data accumulate.

Where Pith is reading between the lines

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

  • Extending beyond the paper: the two rows that use a Gaussian phase prior based on the DAMA best-fit phase may not actually test the DAMA-preferred phase, because the paper's cosine model uses ω(t+t0) while the DAMA fit uses ω(t−t0), shifting the numeric phase peak by about half a year; if so, only the uniform-phase rows are direct tests of a DAMA-phase signal.
  • Extending beyond the paper: Jeffreys' scale's 'barely worth mentioning' label is symmetric, so a log Bayes factor near 1.2 is weak evidence either way and should not be read as a strong rejection of all modulated dark-matter signals.
  • Extending beyond the paper: with the planned 1-ton-year combined exposure, the same model comparison could either push log Bayes factors decisively below zero or reveal a small positive value, making a concrete testable prediction.
  • Extending beyond the paper: applying the same comparison separately to each experiment's six-year dataset could reveal whether the two detectors individually agree in their evidence, rather than only jointly.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. The paper performs a Bayesian model comparison between a sinusoidal annual-modulation model and a constant-background model, using the combined ~3-year COSINE-100 and ANAIS-112 residual data reported by Carlin et al. (2025). Four prior configurations are considered, varying whether the angular frequency and phase use uniform priors or Gaussian priors based on DAMA/LIBRA best-fit values. The evidence integrals are computed with the nested sampler Dynesty. The central claim is that the natural logarithm of the Bayes factor in favor of the cosine model is below 1.15 for both 1-6 keV and 2-6 keV, implying no meaningful evidence for a dark-matter-induced annual modulation. The analysis code is made public.

Significance. If the central claim were fully supported, the paper would provide a useful Bayesian cross-check of the frequentist/MCMC analysis in C25, using the same combined dataset. Public code and well-specified priors are strengths, as is the clear framing as an independent model-comparison test. However, the paper currently contains an internal contradiction between the stated ln B < 1.15 bound and the values in Table I, and the DAMA-normal-prior rows use a phase convention that misplaces the DAMA phase by about two months. The qualitative no-evidence conclusion is likely still supported by the uniform-phase rows, but the DAMA-specific evidence as presented is not reliable.

major comments (3)
  1. [Abstract, Conclusions, and Table I] The abstract and Sec. IV state ln(B21) < 1.15 for all cases, but Table I reports ln B21 = 1.19 for the 1-6 keV row with uniform omega and DAMA-normal phase prior. This is an internal inconsistency in the paper's central quantitative claim. The claim should be corrected to state that no meaningful Bayesian evidence is found, or the table/analysis must be revised so the stated bound actually holds.
  2. [Eq. (4) and Table I, rows 2 and 4] Eq. (4) defines R(t) = S_m cos(omega(t+t0)), whereas Eq. (1) and DAMA/C25 use cos(omega(t-t0)). The footnote acknowledges the sign change but treats it as a harmless convention. It is not. With t0 ~ N(145,5) days imported from DAMA, the model in Eq. (4) peaks at t = -145 mod 365 = 220 days (early August), not near June 2 (day ~153). Rows 2 and 4 therefore place the phase prior ~67 days away from the DAMA-preferred phase and do not test the DAMA-normal hypothesis. Either the phase parameter must be transformed consistently (e.g., model cos(omega t + phi) with phi = -omega t0 and prior on phi derived from t0), or these rows must be relabeled and interpreted as testing a different phase.
  3. [Table I / numerical uncertainty] No uncertainties or convergence diagnostics are reported for the nested-sampling Bayes factors. Since all quoted ln B values are small (between -0.01 and 1.19), even modest numerical errors could affect statements such as 'barely worth mentioning' or comparisons among rows. Reporting the Dynesty evidence error estimates, or at least stating that they are negligible, would strengthen the results.
minor comments (3)
  1. [Table I caption] The caption refers to 'the cosine model in Eq. 1', but the model actually used in the analysis is Eq. (4). Please update the reference.
  2. [Throughout] Several typographical errors: 'refered' in Sec. I, 'assuing' in Sec. III.B, 'laboatory' in Sec. II, and a duplicated 'modulation modulation' near the start of Sec. II. A careful proofreading pass is needed.
  3. [Sec. III.B] The text says uniform priors on amplitude are 'between maximum and minimum value of the observed residuals', while Table I shows U(-max|f_i|, max|f_i|). This is fine, but the wording is imprecise about the use of absolute values.

Circularity Check

0 steps flagged

No significant circularity: the Bayes-factor analysis uses external residuals and external DAMA priors; self-citations are methodological references, not load-bearing reductions.

full rationale

The paper's central claim is a Bayesian model comparison between a cosine modulation model and a constant model, applied to about three years of combined ANAIS-112/COSINE-100 residuals taken from C25. The likelihood and priors are specified independently: DAMA provides the normal priors on angular frequency and phase, and the uniform priors are standard ranges stated in the paper. The resulting Bayes factors are not fitted to reproduce a target conclusion; they are computed quantities reported in Table I. The cited prior works by the same authors are used for methodological continuity (e.g., the uniform phase prior is 'the same as in [13]') and for a sign convention in Eq. 4, but they do not supply the data or the DAMA best-fit values, and they are not invoked to forbid alternatives or to force the conclusion. One mild data dependence exists: the amplitude prior is chosen as U(-max|f_i|, max|f_i|) using the observed residuals themselves. This is an empirical-Bayes style prior choice, and it could influence the evidence, but it does not by construction determine the sign or size of ln B21, since the same data-based prior is used for both models and the Jeffreys-scale outcome is not an algebraic identity. The abstract's statement 'ln(B21) < 1.15' is internally inconsistent with Table I, which reports 1.19 for one prior set, but this is a numerical inconsistency, not circular reasoning. The phase-sign convention in Eq. 4 relative to the DAMA convention in Eq. 1 is a correctness concern for the 'DAMA-normal' prior rows, not a circularity: the model is still evaluated against the data. Overall, the central derivation is self-contained with respect to external data and benchmarks, so no circular step meets the standard of being equivalent to its inputs by construction.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The central Bayes factors rest on the C25 combined residual dataset, a Gaussian independent-error likelihood, and hand-chosen priors. The most fragile inputs are the data-dependent amplitude prior and the DAMA-normal phase prior, applied with a sign convention that shifts the peak by about 2.5 months. No new physics entities are introduced.

free parameters (5)
  • Amplitude prior bound max|f_i| = 0.0789 cpd/kg/keV (1-6 keV), 0.0739 cpd/kg/keV (2-6 keV)
    Uniform prior on modulation amplitude A is set to ±max absolute observed residual; this is data-dependent and affects the Bayes factor normalization.
  • Uniform angular frequency prior bounds = U(0.00455, 0.418) rad/day (period 15-1380 days)
    Chosen by hand from the dataset duration and bin size, not from physics; broad prior dilutes evidence for annual periodicity.
  • DAMA normal prior on omega = N(0.0172, 1.36e-5) rad/day (mean and scale as printed)
    Based on DAMA best-fit period; the printed uncertainty is ambiguous (sigma vs variance) and the conversion from DAMA T=0.999±0.001 year appears misstated in the text.
  • DAMA normal prior on phase = N(145, 5) days
    Used in cos(ω(t+t0)) convention; due to the sign flip in Eq. (4), this prior centers the peak at ~day 220 rather than DAMA's ~day 145.
  • Uniform phase prior = U(0,365) days
    Full phase coverage makes the sign convention irrelevant; this prior drives the robust rows.
axioms (4)
  • domain assumption The 15-day binned residuals from C25 are accurately background-subtracted and are Gaussian-distributed with known, independent errors (Eq. 3).
    The entire likelihood is built on this; no test of Gaussianity or residual correlation is provided.
  • domain assumption The combined exposure/dataset as presented in C25 is correct and complete (485 kg-yr, 1-6 and 2-6 keV).
    The analysis is a re-analysis of C25's residuals; any systematics in that combined dataset propagate directly.
  • domain assumption The annual modulation hypothesis is well represented by a pure cosine R(t)=S_m cos(ω(t+t0)) with no constant offset in M2.
    If background subtraction leaves an offset, the model comparison could favor the constant model for reasons unrelated to modulation.
  • ad hoc to paper DAMA best-fit frequency and phase are appropriate external priors for the signal model.
    Used to define the narrow normal priors; however, the phase prior is applied with the wrong sign convention.

pith-pipeline@v1.3.0-alltime-deepseek · 5223 in / 16837 out tokens · 145718 ms · 2026-08-03T13:41:21.172076+00:00 · methodology

0 comments
read the original abstract

We perform a Bayesian model comparison test between a sinusoidal modulation model and a constant value model using about three years of combined COSINE-100 and ANAIS-112 data. We use both uniform priors and normal priors (based on DAMA best-fit values) for the angular frequency and phase of the cosine signal. We find natural log of Bayes factor for the cosine model compared to the constant value model to be less than 1.15 for the data in both 1-6 keV and 2-6 keV energy intervals. This shows that there is no evidence for cosine signal from dark matter interactions in the combined ANAIS-112/COSINE-100 data. Our analysis codes have also been made publicly available.

discussion (0)

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Reference graph

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