{"id":"e75f23d1-e0cd-4e83-98cc-4def97c3b43b","arxiv_id":"2608.00846","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A Bayesian model-comparison pipeline for position-only trajectories selects the memory-kernel, Mexican-hat, or Brownian model depending on the sampling interval of cell tracks.","lead":"This paper builds a Bayesian framework that selects among competing cell-motion models using only position data, without needing to reconstruct velocities. Applied to Dictyostelium cells, it shows that the statistically favored model changes with the sampling interval, and that coarse sampling makes simpler models look sufficient.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Δt=80 s Mexican-hat selection relies on an approximate likelihood whose nonlinear validity is untested; the supplied OU-only check (Supp. Note 7) does not control the cubic-drift error of Eq. (C12).","rationale":"The reader's weakest assumption—that the transformed-Gaussian approximation is used for the nonlinear Hat model at Δt=80 s without nonlinear validation—is exactly the load-bearing point I find. The paper's central empirical claim is the resolution-dependent model transition; the 5 s all-MK and 640 s all-BM contrast already establishes scale dependence, but the specifically advertised intermediate result is that most DdB trajectories are classified as Hat at 80 s. That classification rests entirely on an approximate likelihood whose error is uncontrolled in the nonlinear regime. I would not move the verdict away from CONDITIONAL: the methodological machinery, the exact-OU likelihood derivation, the importance-sampling convergence check (Fig. 10), and the MSD/VACF consistency at 5 s are genuine supporting evidence, and the authors disclose the main caveats. But the Hat-at-80-s claim should not be treated as robust until a nonlinear validation at DdB-relevant parameters is performed. The concrete test above would settle this directly. It is feasible with the code already released in the repository referenced in the Data Availability statement. No other concern—prior narrowing, post-hoc interval choice, or reuse of MAP parameters for prediction—is as decisive, because those affect interpretation rather than the validity of the likelihood at the exact scale where the nonlinear model wins.","tokens_in":29992,"tokens_out":7489,"duration_ms":104650,"concrete_test":"Calibrate to the DdB regime: draw 100 parameter sets from the Hat posterior ranges shown in Fig. 8 (including both v_r ≤ 0.1 and v_r > 0.1 groups), simulate the Hat SDE at a fine time step (dt = 1 s or finer) with Euler–Maruyama or a higher-order scheme, discard transients, subsample every 80 s, and run the full model-comparison pipeline with the same priors and importance-sampling settings. For at least a subset of these synthetic data sets, compute the Hat evidence with an independent reference that does not use Eq. (C12)—for example, a bootstrap particle filter over latent velocities with fine sub-stepping, or a numerical solution of the Fokker–Planck transition density—and compare the reference log-evidence against the approximate pipeline. If Hat is recovered at roughly the Fig. 1 rate and the approximate evidence agrees with the reference within Monte Carlo error, the concern is re","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most interesting empirical transition—MK at Δt=5 s, Hat at 80 s, BM at 640 s—depends on the Hat model being selected at Δt=80 s. That selection is made with the transformed-Gaussian likelihood of Eqs. (C8)–(C13), which is derived under a small-Δt assumption. The only numerical validation of this approximation is in Supplementary Note 7, and it compares the approximate and exact likelihoods for the OU model only. That check is not probative for the Hat model: for OU, the transformed variable Q in Eq. (C8) is a linear function of the increments, so it is exactly Gaussian; the test only constrains the covariance approximation. For Hat, f(v) = −γv(‖v‖² − v_r²) is cubic, so Q is a nonlinear transform of a Gaussian process and is not Gaussian. No synthetic benchmark in Sec. IV or the supplement exercises this case in the DdB-relevant regime: the Hat benchmarks use Δt=0.1 and the easy condition D/(γv_r^4)<0.3, whereas Fig. 8 shows many inferred trajectories with γv_r² values whose inverse is comparable to or larger than 80 s. At such Δt, omitted higher-order terms in the drift integration can plausibly shift log Bayes factors of the magnitude shown in Fig. 6(b), where the Hat-vs-OU differences are not overwhelming. The concern is amplified by the fact that Δt=80 s was itself chosen from the ring-shaped secant-velocity structure in the same data (Sec. V B); if the approximation error is correlated with ring-like velocities, it would preferentially inflate Hat evidence. This is the single most load-bearing soft spot; the prior-narrowing and post-hoc-interval issues are secondary, and the paper's IS and exact-OU checks are real evidence that the framework itself is sound.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a Bayesian model-comparison framework for second-order Langevin dynamics from position-only trajectories, applied to four candidate models: Brownian motion (BM), integrated Ornstein–Uhlenbeck (OU), Mexican-hat (Hat), and memory-kernel (MK). For the linear Gaussian models, exact increment likelihoods with Toeplitz covariance matrices are used; for the nonlinear Hat model, the transformed-Gaussian approximate likelihood from Ref. [31] is imported. Marginal likelihoods are computed by defensive mixture importance sampling. Synthetic benchmarks at fine sampling recover the generating model (subject to the Mexican-hat identifiability filter D/(γv_r^4)<0.3), and coarse-graining degrades model identifiability. In 261 Dictyostelium discoideum DdB trajectories, all trajectories are classified as MK at Δt=5 s, 200/261 as Hat at Δt=80 s, and 233/261 as BM at Δt=640 s. The selected models are checked against MSD, VACF, and secant-velocity statistics. The paper concludes that the statistically supported model depends strongly on temporal resolution.","tokens_in":30349,"tokens_out":5399,"duration_ms":64665,"significance":"If the result holds, the paper makes a useful methodological contribution: it provides a unified evidence-based pipeline for comparing linear and nonlinear second-order models under partial observation, with exact Toeplitz likelihoods for linear models, an efficient Levinson–Durbin evaluation, a careful importance-sampling convergence check (Fig. 10), and open data/code. The synthetic benchmarks are internally consistent, and the discussion of temporal-resolution-dependent identifiability is honest and well placed. However, the headline empirical transition—MK at 5 s, Hat at 80 s, BM at 640 s—rests on the Hat selection at Δt=80 s, and the validation of the approximate nonlinear likelihood is not yet adequate for that regime. The central claim is defensible in principle, but the manuscript needs additional benchmarks and prior-sensitivity analyses before the empirical conclusion can be accepted.","major_comments":[{"comment":"The transformed-Gaussian likelihood for the Hat model is derived under a small-Δt assumption, but the only numerical validation (Supp. Note 7, Fig. S4) compares approximate and exact likelihoods for the OU model. For OU, Q in Eq. (C8) is an exactly Gaussian linear function of Gaussian increments, so this check tests only the covariance approximation, not the error due to the cubic drift f(v)=−γv(||v||²−v_r²). No synthetic Hat-data benchmark exercises the coarse-Δt, DdB-relevant parameter regime. Since the Hat-vs-OU log Bayes factors at Δt=80 s (Fig. 6b) are not overwhelming, an uncontrolled approximation error could change the ranking. Please validate Eq. (C12) on synthetic Hat data at the inferred parameter values of Fig. 8, e.g. by comparing against a particle-filter or fine-grid likelihood estimate, and report how the Δt=80 s evidence differences change.","section":"Appendix C3, Eq. (C12); Supp. Note 7"},{"comment":"The synthetic Hat benchmark is restricted to trajectories with D/(γv_r^4)<0.3 and Δt=0.1—i.e. the regime where the Mexican-hat peak is well resolved and the drift is slowly varying over one step. The experimental Hat selections at Δt=80 s are based on inferred parameters (Fig. 8) for which this dimensionless smallness condition is not verified; there is no evidence that the benchmark regime covers the inferred parameter distribution. The model-recovery results in Sec. IV therefore do not establish reliability in the regime where the main claim lives. Please report the distribution of the benchmark criterion and a dimensionless measure such as Δt·γv_r² for the 200 selected trajectories, and add coarse-sampled synthetic Hat benchmarks spanning that distribution.","section":"Sec. IV A; Figs. 1, 8"},{"comment":"Bayesian model evidence is prior-dependent, and the model-specific parameters are deliberately given narrower priors to 'enhance model identifiability': v_r ∈ [10^-2, 10^2], u ≥ 2, and s ∈ [0.02, 50], compared with the generic L(10^-4, 10^2) used for shared parameters. The robustness check in Supp. Note 5 varies only the shared parameters and leaves the model-specific priors fixed, so it does not test the prior choice most likely to affect the Hat-vs-OU and MK-vs-OU comparisons. Please add an explicit sensitivity scan over the bounds of v_r, u, and s, and report how many trajectories change classification at Δt=80 s and Δt=5 s.","section":"Sec. III C; Table I; Supp. Note 5"}],"minor_comments":[{"comment":"Typographical issues: 'an second-order' in Sec. II C; 'intergral' in Eq. (7); 'Sepecifically' in Sec. IV B; 'magenda' in the Fig. 6 caption; 'DdB stain' should be 'DdB strain' in Sec. V A.","section":"Throughout"},{"comment":"The predictive checks in Figs. 7 and 9 use MAP parameters inferred from the same trajectories that are being compared. They are valuable consistency checks, but they should be described as in-sample consistency checks rather than as independent predictions, to avoid overstating their confirmatory weight.","section":"Sec. V D"},{"comment":"The stacked-bar figure would benefit from error bars or a table with exact counts and percentages, since the reader's eye cannot easily recover the 200/261 and 233/261 numbers from the figure.","section":"Fig. 5"},{"comment":"The caution about short-time observational noise at Δt=5 s is appropriate. Consider noting explicitly that the same caution applies, with different sign, to the Δt=80 s Hat selection, where the ring-shaped secant-velocity structure was used to choose the analysis scale.","section":"Sec. VI"}],"recommendation":"major_revision","confidential_remarks":"This is a well-executed methods paper with a provisional empirical result. The main risk is not circularity or internal inconsistency, but under-validation of the nonlinear approximate likelihood in exactly the regime where the central claim lives. The authors can likely address this with additional synthetic benchmarks and prior-sensitivity analysis; if those come out clean, the paper should be acceptable for publication. The approximate likelihood originates from a paper co-authored by two of the current authors; this is stated transparently through citation, but the manuscript should make explicit that the only independent numerical validation currently shown is for the linear OU case."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"What you should know: this is a useful and honest methods paper. The framework—exact increment likelihoods for the linear Gaussian models, the transformed-Gaussian approximation for the nonlinear one, and importance sampling with convergence diagnostics—is coherent and well tested on synthetic data. The central empirical finding, that the supported model changes with sampling interval (MK at 5 s, Hat at 80 s, BM at 640 s), is striking and robust in its qualitative form: the same coarse-graining trend appears across three additional strain conditions in the supplement. The IS-against-direct-integration check (Fig. 10) and the approximate-vs-exact OU likelihood comparison (Fig. S4) are real evidence that the machinery works, and the data/code are open.\n\nThe load-bearing soft spot is the Hat selection at 80 s. The transformed-Gaussian likelihood is derived under a small-Δt assumption. The only numerical validation of that approximation is for the OU model, which is not probative: for OU the transformed variable is a linear function of the increments, so it is exactly Gaussian—the check only constrains the covariance approximation. The Hat model's cubic drift makes Q genuinely non-Gaussian, and no synthetic benchmark exercises this in the DdB-relevant regime. The Hat benchmarks use Δt=0.1 and restrict to D/(γv_r^4)<0.3, excluding the hard-to-identify cases; at Δt=80 s the inferred parameters put many trajectories where the expansion is strained. The Bayes factors separating Hat from OU at 80 s are not overwhelming, so I would read the 200/261 Hat assignment as suggestive rather than established.\n\nThe secondary concerns are real but minor. The priors for model-specific parameters (v_r, u, s) are deliberately narrowed; the paper discloses this, but it can inflate evidence differences. The three sampling intervals were chosen after inspecting MSD, DACF, and velocity distributions from the same data; the qualitative loss-of-identifiability conclusion does not depend on the exact choices. The \"prediction\" checks reuse MAP parameters from the same trajectories—a consistency check, not out-of-sample prediction—and the paper mostly frames them that way.\n\nWho this is for: single-particle-tracking practitioners and anyone doing Bayesian model selection for partially observed stochastic dynamics. It deserves a serious referee. The main revision request should be a synthetic Hat benchmark at the relevant Δt, or an explicit caveat that the 80 s Hat evidence is conditional on an unvalidated approximation. I would cite the framework and would bring it to a reading group.\n\nRecommendation: send to peer review with the nonlinear-validity gap as the key issue to resolve.","headline":"A solid, carefully built model-comparison toolkit for position-only Langevin inference; the resolution-dependence result is real, but the Mexican-hat selection at Δt=80 s rests on an approximate likelihood whose nonlinear validity is not checked.","tokens_in":30932,"tokens_out":1944,"would_cite":true,"duration_ms":23309,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that the statistically supported Langevin model for Dictyostelium cell motion depends on sampling interval: memory-kernel at 5 s, Mexican-hat at 80 s, Brownian at 640 s.","keywords":["Bayesian model comparison","Langevin dynamics","position-only inference","cell motility","Dictyostelium discoideum","temporal resolution","model evidence","memory-kernel model"],"falsifier":"Generate synthetic Mexican-hat trajectories with the MAP parameter ranges and sample them at Δt = 80 s; if the framework no longer recovers the Mexican-hat model at the rate reported for fine sampling, the 80-s conclusion rests on the approximation rather than on the data. A direct check would compare exact versus transformed-Gaussian marginal likelihoods for the OU model under the same coarse sampling with parameters in the Hat regime, which the supplementary validation does not currently do.","tokens_in":29831,"feed_emoji":"🧫","tokens_out":6462,"duration_ms":57782,"temperature":0.7,"pith_summary":"This paper builds a Bayesian model-comparison framework for second-order Langevin dynamics when only positions are observed, not velocities. It ranks four candidate models—Brownian motion, integrated Ornstein-Uhlenbeck, the nonlinear Mexican-hat preferred-speed model, and a linear memory-kernel model—through marginal likelihoods computed on positional increments with latent velocities integrated out. On synthetic data the true generating model is recovered at fine sampling, and identifiability degrades as the sampling interval grows. Applied to 261 Dictyostelium discoideum tracks, the winning model shifts with temporal resolution: all trajectories favor the memory-kernel model at 5 s, most favor the Mexican-hat model at 80 s (with ring-shaped secant-velocity distributions), and most are indistinguishable from Brownian motion at 640 s.","feed_headline":"Sampling rate decides which motion model fits Dictyostelium cells","feed_subtitle":"A Bayesian comparison of 261 cell tracks shows the winning model depends on how often positions are recorded.","key_machinery":"The central object is the positional increment process Δr_i = r_{i+1} − r_i, with the latent velocity integrated out. For the linear Gaussian OU and memory-kernel models this yields exact multivariate-Gaussian increment likelihoods with Toeplitz covariance matrices; for the nonlinear Mexican-hat model it yields the transformed-Gaussian approximate likelihood of Ref. [31]. Marginal likelihoods are evaluated by importance sampling with a defensive Gaussian-mixture-plus-prior proposal, and models are ranked by log Bayes factors.","core_discovery":"The paper's central claim is that evidence-based model selection for partially observed stochastic dynamics must be done on the increment process, not by substituting reconstructed velocities, and that when this is done the supported model class is a function of the observation scale. For linear Gaussian models the position increments are jointly Gaussian with analytically known Toeplitz covariance matrices, giving exact likelihoods; for the nonlinear Mexican-hat model the paper adopts a transformed-Gaussian approximation that treats a nonlinear transformation of the secant velocities as Gaussian with a tridiagonal covariance. The framework is validated on synthetic trajectories and then app","pith_inferences":["Observational noise or tracking artifacts at 5 s could masquerade as a memory kernel; an explicit observation-noise likelihood is the natural next test and would clarify whether the fine-scale memory-kernel selection is dynamical or instrumental.","The resolution dependence implies that published model-selection results from cell tracks may disagree simply because of different frame rates; re-analyzing datasets at matched temporal resolution could resolve apparent contradictions.","The 5-s memory-kernel and 80-s Mexican-hat selections suggest that coarse-graining does not preserve model family, so a model combining a memory kernel with nonlinear preferred-speed friction is a plausible candidate for a single description spanning all scales.","The Toeplitz exact-likelihood machinery for linear Gaussian models could be reused for other latent-state linear systems, e.g., tracking with hidden internal states, without re-deriving inference from scratch."],"forward_implications":["At Δt = 5 s, the inferred memory-kernel models reproduce both the MSD and the velocity autocorrelation of the DdB trajectories, supporting the presence of at least two characteristic time scales in finely sampled cell motion.","At Δt = 80 s, the 200 trajectories assigned to the Mexican-hat model split by inferred preferred speed, and the subgroup with v̂r > 0.1 µm/s shows a ring-shaped secant-velocity distribution consistent with preferred-speed dynamics.","At Δt = 640 s, 233 of 261 trajectories are statistically indistinguishable from Brownian motion; effective diffusion coefficients estimated from long memory-kernel-generated trajectories match the empirical MSD better than direct subsample estimates.","The same coarse-graining trend appears across other Dictyostelium strains and conditions, indicating it is a general feature of position-only inference rather than an artifact of one dataset.","The framework is applicable beyond cell motility to any second-order stochastic system observed only through part of its state, once a positional-increment likelihood is available."],"supporting_citations":[{"why":"supplies the transformed-Gaussian approximate positional-increment likelihood used for the nonlinear Mexican-hat model","marker":"[31]"},{"why":"reports the ring-shaped velocity distribution in Dictyostelium that motivates the Mexican-hat/preferred-speed model","marker":"[17]"},{"why":"introduces the preferred-speed (Mexican-hat) model with nonlinear velocity-dependent friction","marker":"[18]"},{"why":"reviews active Brownian particle models and provides the preferred-speed and OU reference descriptions","marker":"[19]"},{"why":"provides the exact Gaussian increment likelihood with Toeplitz covariance for linear Gaussian single-particle tracking models","marker":"[28]"},{"why":"motivates the memory-kernel model by reporting double-exponential decay of the velocity autocorrelation in cell motility","marker":"[12]"},{"why":"exemplifies model-selection methods that assume full state observation, the gap this framework fills","marker":"[25]"}],"fun_headline_variants":["Sampling rate flips which motion model fits Dictyostelium cells","Bayesian model choice for cell motion hinges on sampling interval","Temporal resolution decides winning Langevin model for cell tracks","How often you sample changes the best model for cell motility","Position data alone: Bayesian test picks model based on sampling rate"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The approximate likelihood used for the nonlinear Mexican-hat model is derived for small sampling intervals, yet the key experimental result uses it at 80 s, where the nonlinear drift term may fall outside the approximation's validity.","fun_headline_variants_meta":{"raw":{"variants":["Sampling rate flips which motion model fits Dictyostelium cells","Bayesian model choice for cell motion hinges on sampling interval","Temporal resolution decides winning Langevin model for cell tracks","How often you sample changes the best model for cell motility","Position data alone: Bayesian test picks model based on sampling rate"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000525,"raw_usage":{"total_tokens":2321,"prompt_tokens":642,"completion_tokens":1679,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":386,"completion_tokens_details":{"reasoning_tokens":1593}},"tokens_in":386,"tokens_out":1679,"duration_ms":14008,"temperature":1.0,"reasoning_tokens":1593,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T00:10:00.735724+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate synthetic Mexican-hat trajectories with the MAP parameter ranges and sample them at Δt = 80 s; if the framework no longer recovers the Mexican-hat model at the rate reported for fine sampling, the 80-s conclusion rests on the approximation rather than on the data. A direct check would compare exact versus transformed-Gaussian marginal likelihoods for the OU model under the same coarse sampling with parameters in the Hat regime, which the supplementary validation does not currently do.","supporting_citations":[{"cited_title":"Boninsegna, F","cited_arxiv_id":null,"evidence_quote":"supplies the transformed-Gaussian approximate positional-increment likelihood used for the nonlinear Mexican-hat model"},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"reports the ring-shaped velocity distribution in Dictyostelium that motivates the Mexican-hat/preferred-speed model"},{"cited_title":"Kapate, R","cited_arxiv_id":null,"evidence_quote":"introduces the preferred-speed (Mexican-hat) model with nonlinear velocity-dependent friction"},{"cited_title":"Klages, Cell migration: Beyond Brownian motion, Biophysical Journal123, 1167 (2024)","cited_arxiv_id":null,"evidence_quote":"reviews active Brownian particle models and provides the preferred-speed and OU reference descriptions"},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides the exact Gaussian increment likelihood with Toeplitz covariance for linear Gaussian single-particle tracking models"},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"motivates the memory-kernel model by reporting double-exponential decay of the velocity autocorrelation in cell motility"},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"exemplifies model-selection methods that assume full state observation, the gap this framework fills"}],"review_version":1}