{"id":"c770b284-0dca-43e1-a15a-2025e2f093d8","arxiv_id":"2607.21484","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A single RJMCMC run can rank BBH, NSBH, and BNS waveform models and deliver the favored model's parameter posteriors, validated on injections and two real GW events.","lead":"The paper introduces t-roo, a sampler that compares different gravitational-wave source models in a single run by jumping between models as a Markov chain parameter. It is tested against the standard dynesty sampler on simulated signals and applied to two real events whose source type was uncertain.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (19) cancellation g'/g·J=1 is asserted but not established for the data-dependent mass/tidal maps; the inverse proposals in Appendix B.1 are implicit in Mc/q and no invertibility range is given, so the sampler's stationary distribution may not be the intended posterior.","rationale":"Good-faith reading: the paper's contribution is a reusable RJMCMC sampler; the central claim is that it computes correct odds ratios/posteriors in one run, validated against dynesty. I focused on the acceptance probability because if Eq. (19) fails no amount of empirical agreement can rescue the method. The forward map and Jacobian computation are plausible; credit is due for including pseudo-parameters in the prior and for the detailed Appendix B. However, the reverse maps in B.1 are stated as 'simply the inverse' without proof. The formulas for Mc/q are implicit: the new \\tildeΛ on the RHS depends on the quantity being solved for. The stated reversibility condition (u w = 1) only guarantees the tidal parameters round-trip, not the full state, because \\tildeΛ also depends on Mc and q. This is a concrete mathematical gap, not a disagreement with consensus. If the implemented inverse is not exact, the chain is not reversible and the model fractions from Eq. (2) are not posterior probabilities. The validation contradiction in Table II (nsbh lam600 lowsnr: t-roo lnO=-0.86 vs dynesty +0.40±0.27) is a symptom consistent with this concern, though it could also be a typo or convergence issue. Because the issue is addressable by a direct numerical round-trip test, conditional/unchanged is appropriate pending that check.","tokens_in":38458,"tokens_out":18190,"duration_ms":162518,"concrete_test":"Write a numerical round-trip test using the actual t-roo proposal code (or a standalone implementation of Eqs. 15-17 and B14-B16): draw N=10^5 states and auxiliary variables from the proposal distributions across the prior range for a representative injection (e.g., nsbh lam600), apply the forward map then its claimed inverse, and measure max/mean deviation ||F^{-1}(F(x,u))-x|| and the local Jacobian g'/g·J via finite differences. If deviations exceed machine precision or g'/g·J differs from 1 by >1%, Eq. (19) fails; alternatively, if round-trip is exact, rerun the sampler with the inverse map replaced by a root-finding solution of the fixed-point equation and compare odds ratios. This settles whether the stationary distribution is the intended posterior.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (single run returns correct odds ratios) rests on Eq. (19): g'/g·J=1 for every between-model jump. The forward maps in Eqs. (15)-(17) are explicit, and the Jacobian in Appendix B.2 is computed for these maps. But reversibility also requires that the 'inverse' maps in Eqs. (B14)-(B16) are true inverses. Those inverse formulas are not explicit: they define the new Mc and q through \\tildeΛ of the new state, e.g. M'_c,bns = M_c,bbh + s_Mc \\tildeΛ'_bns, and \\tildeΛ depends on M_c and q themselves. The paper only states that u1w1=1 assures \\tildeΛ'_bns=\\tildeΛ_bns, which is circular. Unless the fixed-point equation (M'_c,q') = (M_c,q) + s(\\tildeΛ'-\\tildeΛ) has the old state as its unique solution (true only under a contraction condition on s_Mc ∂\\tildeΛ/∂M_c + s_q ∂\\tildeΛ/∂q), the implemented reverse jump is not the inverse, detailed balance is broken, and Eq. (19) is false. No ranges of s_Mc, s_q for global invertibility are given, and the code (GitHub link malformed) cannot be checked. Since every odds ratio and posterior in Table II inherits this, the validation 'agreement with dynesty' is not evidence for correctness if the acceptance probability is wrong.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents t-roo, a reversible-jump MCMC sampler, built on eryn and Bilby, for transdimensional inference on gravitational-wave signals from compact binary coalescences. The sampler is designed to compare BBH, NSBH, and BNS waveform models with different parameter-space dimensionalities, returning both model probabilities/odds ratios and parameter posteriors in a single run. The between-model proposals use stretch moves for tidal parameters and data-informed linear maps for chirp mass and mass ratio, with the slopes estimated in a preliminary sampling phase. The authors validate t-roo on a set of injections and on two real events, comparing model odds and posteriors with dynesty, and claim agreement in the preferred models in all tests. The central mathematical claim is Eq. (19), that the auxiliary-variable ratio times the Jacobian equals 1, which is used to simplify the acceptance probability.","tokens_in":38913,"tokens_out":20336,"duration_ms":166231,"significance":"If correct, this would be a valuable new tool for gravitational-wave model selection, potentially reducing the cost of comparing many models or highly informative signals by performing one transdimensional run instead of separate nested-sampling runs. The paper includes useful details, such as pseudo-parameters that cache tidal information and a careful argument that priors on those pseudo-parameters must be included in the acceptance ratio (Appendix B4). The approach is well-motivated and the comparison infrastructure is standard. However, the central reversibility argument is not established: the Jacobian computation omits a term, the inverse between-model maps are not shown to be true inverses, and the tidal-proposal equations contain apparent typos. These issues directly affect the sampler's stationary distribution and therefore every reported odds ratio. The validation overclaim in Section V (and the abstract) is also contradicted by Table II. The underlying idea is promising, but the mathematical core needs substantial correction before the sampler's outputs can be trusted.","major_comments":[{"comment":"The Jacobian derivation omits the dependence of the mass-ratio proposal on the mass ratio itself. For the BNS→BBH map in Eq. (16), q_bbh = q_bns − s_q \\tildeΛ(Mc,q,Λ1,Λ2), so ∂q_bbh/∂q_bns = 1 − s_q ∂\\tildeΛ/∂q, not 1. The Mc-row also has ∂Mc_bbh/∂q_bns = −s_Mc ∂\\tildeΛ/∂q. Including these terms gives det J = (1 − s_q ∂\\tildeΛ/∂q)/(w1 w2), not 1/(w1 w2). Hence Eq. (19) should read g'/g·J = 1 − s_q ∂\\tildeΛ/∂q, which is not 1 in general (e.g., for unequal tidal deformabilities). This directly biases the acceptance probability in Eq. (18) and all model probabilities in Table II. The authors must provide the corrected Jacobian or prove that ∂\\tildeΛ/∂q = 0.","section":"Appendix B2, Eq. (B18) and Eq. (19)"},{"comment":"The inverse transformations in Eqs. (B15)–(B16) are not demonstrated to be the true inverses of Eqs. (15)–(17). For example, the inverse BNS→BBH defines M'_c,bns via M'_c,bns = M_c,bbh + s_Mc \\tildeΛ(M'_c,bns, q'_bns, ...), which is a fixed-point equation in the new masses. The condition u1w1 = 1 recovers the old tidal parameters, but it does not imply M'_c,bns = M_c,bns or q'_bns = q_bns; the statement in Eq. (B13) that reversibility follows from \\tildeΛ_bns = \\tildeΛ'_bns is circular. No contraction condition or uniqueness proof is given, and no invertibility range for s_Mc and s_q is provided. Without a genuine diffeomorphism h, the proposal pair does not satisfy the measure-matching requirement of Green's reversible-jump construction, so detailed balance is broken regardless of the Jacobian factor.","section":"Appendix B1, Eqs. (B12)–(B16)"},{"comment":"The tidal-parameter proposals appear to contain typos. In Eq. (16), Λ2,bbh,i+1 is proposed as Λ2,j,i + w2(Λ1,bns,i − Λ2,j,i) rather than using Λ2,bns,i; the same pattern appears in Eq. (17) and in the inverse formulas (B15)–(B16), where Λ1 is used for both Λ1 and Λ2. If implemented literally, the transformation is not reversible: with u2=1/w2 the inverse gives Λ2,bns' = Λ2,j + u2(Λ1,bns − Λ2,j), which equals the original Λ2,bns only when Λ1,bns = Λ2,bns. The stated reversibility conditions u2w2=1 and v2w2=1 are therefore insufficient. Please correct the equations and verify that the code uses the intended component tidal deformability.","section":"Eqs. (16)–(17) and (B15)–(B16)"},{"comment":"The claim 'in all the tests, the model preferred by t-roo and dynesty is the same' is contradicted by Table II. For nsbh lam600 lowsnr, t-roo gives lnO_{bbh}^{nsbh} = −0.86 (NSBH preferred) while dynesty gives +0.40 (BBH preferred). In the bns lam600 mm row, t-roo prefers IMRPhenomD NRTidalv2 over IMRPhenomXAS NRTidalv3 (lnO = +0.065) whereas dynesty prefers XAS NRTidalv3 (lnO = −0.22). The text in Sec. V C acknowledges the second discrepancy but the abstract and Sec. V overstate the agreement. This validation claim must be qualified, and the low-SNR discrepancy explained.","section":"Section V, Table II, abstract"}],"minor_comments":[{"comment":"The GitHub URL 'https://github.com/AnnaPuecher/t roo' contains a space and is not clickable; it should be a valid repository link (e.g., with a hyphen or underscore). This hampers reproducibility.","section":"Section I, footnote 1"},{"comment":"The proposal distributions g(z) are written as 1/√z without a normalization constant. The normalization cancels in the acceptance ratio, but as written they are not probability densities. Please state that they are defined up to normalization, or include the normalizing factor.","section":"Eq. (9) and Eq. (4)"},{"comment":"The matrix notation is ambiguous: Θ is a vector, so the displayed block is not literally 6×6; the absolute-value bars inside individual entries of the Jacobian are also nonstandard. Please present the Jacobian with clear block notation and take the absolute value only of the final determinant.","section":"Appendix B2, Eq. (B17)"},{"comment":"There are several typographical errors, e.g., 'starey' after Eq. (18), 'dynetsyrecover' in Sec. V B, and inconsistent notation for the tidal parameters in the equations noted above. A careful proofreading pass is needed.","section":"General"},{"comment":"The computational-advantage argument is weakened by the authors' own statement that 'eryn does not scale properly when running on more than 8 cores' and that dynesty can run in parallel on many CPUs. This is acknowledged, but it should be more prominently reflected in the abstract and conclusions.","section":"Section V E"}],"recommendation":"major_revision","confidential_remarks":"The core reversibility proof appears incorrect: the Jacobian in Appendix B2 misses a term in the mass-ratio derivative, and the inverse between-model maps are not shown to be genuine inverses. These are load-bearing issues for every reported odds ratio. The validation overclaim in Section V/abstract is also contradicted by Table II. I recommend major revision rather than rejection because the overall idea is promising and the issues may be fixable with a corrected derivation and, possibly, a redesigned between-model proposal. The authors should also fix the apparent typos in the tidal proposals and provide a working code link."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing you should know: this is the first RJMCMC sampler for full CBC signals with state-of-the-art waveforms, and it is not a toy. The pseudo-parameter storage idea and the data-informed Mc/q proposals are genuinely new, and the authors put real work into the implementation and testing on injections, ET, and real events. Second thing: the central detailed-balance claim (Eq. 19) is not actually established. The inverse mass proposals in Appendix B.1 are implicit, and the paper's proof that they are inverses is circular.\n\nThe good parts: the sampler builds on eryn and Bilby, is public (though the GitHub link is malformed), and the authors validate across multiple waveform models, SNRs, and against dynesty. The RJMCMC machinery is derived in more detail than usual in this literature, and the empirical comparison is extensive. That effort is real.\n\nThe soft spots are serious. In B.1 the forward BNS->BBH map uses Lambda-tilde of the old state, but the inverse BBH->BNS map uses Lambda-tilde of the proposed state. The authors claim u1w1=1 and u2w2=1 make Lambda-tilde' = Lambda-tilde, but those conditions only invert the tidal parameters. Lambda-tilde also depends on Mc and q, so the inverse map is a fixed-point equation. No version of the paper proves that this equation has the old state as its unique solution, or even that it has a solution. Without that, the acceptance probability in Eq. (18) is not the one that gives the intended posterior, and all odds ratios in Table II are suspect.\n\nThe validation data already contain a warning. Table II's 'nsbh lam600 lowsnr' row gives lnO_bbh/nsbh = -0.86 from t-roo and +0.40 from dynesty; t-roo prefers NSBH, dynesty prefers BBH. That directly contradicts the statement in Section V that in all tests the preferred model is the same. Appendix D also reports pymultinest strongly favoring BBH for nsbh lam600, which the paper mentions but does not resolve. These are not minor discrepancies; they are exactly where the fixed-point bias would show up.\n\nOn the positive side, the idea is worth taking seriously. If the fix is to add a Jacobian for the implicit map, or to impose a contraction condition on the slopes, the method could be very useful for next-generation detectors. As written, I would not trust its odds ratios. It deserves a serious referee, not a desk reject, and the referee should be asked to verify the detailed balance and explain the lowsnr row.\n\nRecommendation: send to peer review, with the expectation of major revision.","headline":"A genuinely new RJMCMC sampler for CBC model selection, but the detailed-balance proof has a real gap and the validation contradicts itself on the low-SNR run.","tokens_in":39381,"tokens_out":8015,"would_cite":false,"duration_ms":70230,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A single reversible-jump MCMC run can compare gravitational-wave source models and return odds ratios, matching standard nested sampling.","keywords":["reversible jump MCMC","model selection","gravitational waves","compact binary coalescence","neutron star classification","Bayesian evidence","source identification","transdimensional inference"],"falsifier":"Take a simulated signal with a known model and known evidence, run t-roo alongside a reliable evidence computation, and check whether the odds ratio from sample fractions matches the evidence ratio within sampling error — especially for signals where the learned slopes are steep or the mass/tidal support is widely separated. Alternatively, evaluate Eq. (19) numerically over the full prior range of the auxiliary variables and slopes; any deviation from 1 falsifies the sampler's correctness.","tokens_in":38380,"feed_emoji":"🦘","tokens_out":3791,"duration_ms":38097,"temperature":0.7,"pith_summary":"The paper presents t-roo, a sampler that treats the waveform model itself as a parameter to be jumped between, so one analysis returns both the odds ratio between competing source descriptions and the parameter posteriors for the favored ones. It targets the question that often decides gravitational-wave source classification: was the compact object a black hole, a neutron star, or a neutron star–black hole pair? The authors validate the sampler on simulated signals and on two real ambiguous events, finding that the model it prefers matches the ranking from a standard nested-sampling analysis. If the method holds up, it makes model comparison cheaper as data become more informative, because the sampler automatically spends most iterations in the model the data favor.","feed_headline":"One sampler run ranks gravitational-wave source models","feed_subtitle":"One run yields model odds and posteriors together, agreeing with standard nested-sampling rankings.","key_machinery":"The between-model move: a reversible jump between models with different numbers of tidal parameters, using storage tidal parameters in models that do not use them, a stretch move with tiny jumps for the tidal variables, and slopes learned from a short preliminary sampling phase to map chirp mass and mass ratio between models. The identity that carries the argument is Eq. (19): the ratio of auxiliary-variable densities times the Jacobian equals one, so detailed balance survives without extra factors.","core_discovery":"The central claim is that transdimensional inference for compact-binary gravitational-wave signals is practical with a carefully designed reversible jump sampler. The sampler jumps between models of different parameter-space dimension, using pseudo-parameters to cache tidal deformability information between jumps, data-informed linear maps for chirp mass and mass ratio tied to tidal deformability, and auxiliary-variable constructions for which the proposal-density ratio and Jacobian cancel exactly, so the acceptance ratio reduces to likelihood and prior ratios. In every injection test the sampler's preferred model matches the reference nested sampler, and on the two ambiguous real events it","pith_inferences":["The design suggests a general recipe: any model-comparison problem with nested parameter spaces could use the same pseudo-parameter caching and learned linear maps, not just compact-binary source classes.","Because exactness of the Jacobian cancellation is asserted rather than numerically demonstrated across the full proposal range, a targeted check of the acceptance ratio against known Bayes factors would strengthen the central claim.","The BNS-versus-NSBH degeneracy at leading tidal order implies the sampler's classification probabilities may approximate which waveform family fits best rather than a definitive astrophysical composition; models that distinguish individual tidal deformabilities will sharpen the physical interpretation.","The computational advantage depends on parallelization improvements; the current implementation has overhead that limits scaling, so actual speedups may be smaller than the single-run savings suggest."],"forward_implications":["One analysis yields both model odds and posteriors for favored models, replacing separate runs per model.","For informative, high-signal-to-noise events the sampler converges quickly to the favored model, cutting cost exactly where traditional analyses get expensive.","Source classification for ambiguous events can be read directly from sampling fractions, giving probabilities for black-hole, neutron-star, and mixed systems.","Comparing many models at once is feasible; disfavored models receive fewer samples, and the ranking matches a standard nested-sampling reference.","The approach extends to next-generation detectors, where separate analyses of loud, long signals would be computationally prohibitive."],"fun_headline_variants":["Tipsy kangaroo jumps between gravitational-wave models in one run","One MCMC run ranks gravitational-wave source models and parameters","Kangaroo sampler hops across models for gravitational-wave astronomy","Single sampler leap: model odds and posteriors for gravitational waves","Transdimensional MCMC picks gravitational-wave model in one pass"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"Everything rests on the exact cancellation in Eq. (19) — that the auxiliary-variable density ratio times the Jacobian equals one for every proposed jump, and on the learned mass/tidal mapping being invertible; if that fails, the sampler's stationary distribution is no longer the intended posterior and all model probabilities are biased.","fun_headline_variants_meta":{"raw":{"variants":["Tipsy kangaroo jumps between gravitational-wave models in one run","One MCMC run ranks gravitational-wave source models and parameters","Kangaroo sampler hops across models for gravitational-wave astronomy","Single sampler leap: model odds and posteriors for gravitational waves","Transdimensional MCMC picks gravitational-wave model in one pass"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000175,"raw_usage":{"total_tokens":1149,"prompt_tokens":799,"completion_tokens":350,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":543,"completion_tokens_details":{"reasoning_tokens":267}},"tokens_in":543,"tokens_out":350,"duration_ms":4329,"temperature":1.0,"reasoning_tokens":267,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T07:17:55.117270+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a simulated signal with a known model and known evidence, run t-roo alongside a reliable evidence computation, and check whether the odds ratio from sample fractions matches the evidence ratio within sampling error — especially for signals where the learned slopes are steep or the mass/tidal support is widely separated. Alternatively, evaluate Eq. (19) numerically over the full prior range of the auxiliary variables and slopes; any deviation from 1 falsifies the sampler's correctness.","supporting_citations":[],"review_version":1}