Pith. sign in

REVIEW 3 major objections 4 minor 72 references

Bayesian comparison of Langevin dynamics for cell motility from positional observation

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2608.00846 v1 pith:66D2BQJB submitted 2026-08-01 q-bio.CB nlin.AOphysics.bio-phstat.ME

Yusuke Kato , Jan Albrecht , Ted Moldenhawer , Robert Grossmann , Carsten Beta This is my paper · ORCID
classification q-bio.CBnlin.AOphysics.bio-phstat.ME
keywords BayesianmodelcomparisonLangevindynamicsposition-onlyinferencecellmotilityDictyosteliumdiscoideumtemporalresolutionevidencememory-kernel
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 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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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.

Referee Report

3 major / 4 minor

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.

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 (3)
  1. [Appendix C3, Eq. (C12); Supp. Note 7] 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.
  2. [Sec. IV A; Figs. 1, 8] 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.
  3. [Sec. III C; Table I; Supp. Note 5] 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.
minor comments (4)
  1. [Throughout] 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.
  2. [Sec. V D] 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.
  3. [Fig. 5] 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.
  4. [Sec. VI] 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.

Circularity Check

1 steps flagged · score 2.0 of 10

Core model comparison is self-contained; one in-sample consistency check is overlabeled as an independent prediction.

  1. fitted input called prediction [Sec. V D ('Prediction from selected models'), p. 9; see also Fig. 7 and abstract]
    "To further assess whether the selected models provide a quantitatively consistent description of the DdB trajectories, we test whether they can reproduce the corresponding trajectory statistics using the inferred parameters. The resulting model predictions are shown as red dashed curves in Fig. 7 (a) and (b), together with the empirical statistics computed directly from the DdB trajectories (solid curves)."

    The 'predictions' are evaluated on the same data used to infer the MAP parameters (Eq. 10, Fig. 11). For the memory-kernel model, the increment likelihood (Eq. 16) is built from the Toeplitz covariance (Eq. C6), which is a double time-integral of the model VACF (Eq. A11); the predicted MSD (Eq. A13) is the same VACF integrated twice, and the predicted VACF is Eq. (A11) itself. The empirical MSD and VACF are computed from the same DdB trajectories (Eqs. 19-21). Thus the comparison is an in-sample goodness-of-fit: the parameters were chosen to match the observed increment covariance, and the 'predicted' MSD/VACF are deterministic functions of that same fitted covariance. The agreement is therefore largely forced by the fit, not an independent out-of-sample prediction. The abstract's claim th

full rationale

The central derivation is not circular: exact Gaussian increment likelihoods for the OU and memory-kernel models are obtained by integrating their stationary velocity autocorrelation functions (Eqs. C4-C6), the BM likelihood is exact, and synthetic benchmarks independently validate model recovery at fine sampling (Fig. 1) and quantify loss of identifiability under coarse sampling (Fig. 2 and Fig. S3). The Mexican-hat likelihood uses the transformed-Gaussian approximation of Ref. [31] (Eqs. C8-C13). Although this is a self-citation (Albrecht and Großmann are co-authors) and the approximation's nonlinear validity at Δt=80 s is not directly tested, this is a correctness/robustness concern rather than a circularity: no equation defines the Hat evidence in terms of its own output, and the paper explicitly discusses the small-Δt assumption and low-ESS caveats. The deliberate narrowing of model-specific priors (Table I, Sec. III C) is a stated modeling choice with a robustness check in Supp. Note 5, not a hidden fit. The one genuine circularity is the 'Prediction from selected models' section, which re-labels an in-sample posterior consistency check as predictive support. This is a minor overstatement and does not drive the main temporal-resolution finding, so the circularity score is low.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The framework itself introduces no new physical entities; all models are from the literature. The main 'inputs pulled from upstream' are the approximate likelihood (from co-authored Ref. [31]) and prior choices that partly determine model-comparison outcomes. The free parameters are model parameters fit to each trajectory, plus a filter on synthetic Hat trajectories that avoids difficult identification regimes.

free parameters (4)
  • D, gamma (OU, Hat) = MAP-estimated per trajectory (e.g., Fig. 8, Fig. 11)
    Diffusion coefficient and damping rate are estimated from data via MAP; central to the likelihood.
  • v_r (Hat) = MAP-estimated per trajectory, split at 0.1 µm/s in Fig. 8
    Preferred speed in the Mexican-hat model; a model-specific parameter with a narrower prior to enhance identifiability.
  • d1, u, s (MK) = MAP-estimated per trajectory (Fig. 11 shows d1, d2)
    Reparametrization of MK model: smaller decay rate, ratio of decay rates, ratio of VACF amplitudes. Log-uniform priors with u lower bounded at 2 to separate MK from OU.
  • D/(γ v_r^4) < 0.3 filter = Not fitted; a selection criterion
    Used when generating synthetic Mexican-hat trajectories; restricts to parameter sets where the ring-shaped velocity distribution is resolvable, excluding hard-to-identify regimes from the benchmark.
assumptions (4)
  • domain assumption Stationary initial condition: p(V0|θ) is approximated by the stationary distribution of the instantaneous velocity
    Appendix C 3, before Eq. (C12); ignores transient/initial-condition effects in the likelihood approximation.
  • domain assumption The transformed-Gaussian approximation (Eqs. C8-C13) holds for the Mexican-hat model at the sampling intervals used (notably Δt=80 s)
    This approximation from Ref. [31] assumes small Δt; the paper validates it on the OU model but not on the nonlinear model at coarse sampling.
  • standard math Positional increments of the linear Gaussian models are jointly Gaussian with Toeplitz covariance
    Standard Gaussian process property; used for exact likelihoods in Sec. III B 2 and Appendix C 2.
  • domain assumption Memory-kernel stability condition aγ > A holds
    Eq. (5); required for a stable stationary process; used implicitly in parameter priors and VACF formulas.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Bayesian comparison of Langevin dynamics for cell motility from positional observation." pith.science (2026). https://pith.science/paper/66D2BQJB

@misc{pith2026260800846,
  author       = {Pith},
  title        = {Pith review of: Bayesian comparison of Langevin dynamics for cell motility from positional observation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/66D2BQJB}},
  note         = {Machine review of arXiv:2608.00846}
}
read the original abstract

We develop a Bayesian framework for model comparison of second-order Langevin dynamics from position-only trajectories. While approximate increment likelihoods for nonlinear position-only inference have been formulated previously, a unified evidence-based framework for comparing multiple second-order models under positional observation has remained lacking. Here we address this problem by combining exact increment likelihoods for linear Gaussian models with a previously proposed approximate likelihood for nonlinear dynamics. Synthetic-data benchmarks show reliable recovery of the generating model at fine sampling intervals and progressive loss of identifiability under coarse temporal sampling. Application to Dictyostelium discoideum trajectories demonstrates that the statistically supported model depends strongly on temporal resolution. Moreover, the selected models reproduce key statistical properties of the experimental trajectories, providing additional support for the model-comparison results. Our framework therefore offers a practical approach to evidence-based comparison of partially observed stochastic dynamics.

Figures

Figures reproduced from arXiv: 2608.00846 by the authors.

Figure 1
Figure 1. FIG. 1. Results of model comparison from synthetic trajecto [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Dependence of model comparison on the sampling in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Preliminary analysis of DdB cell trajectories. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Velocity distributions of DdB cells for different finite [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Counts of selected models across sampling intervals. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Log Bayes factors for model comparison from DdB [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Comparison of empirical trajectory statistics with [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Parameter estimates and velocity distributions for [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Distribution of inferred parameters and MSDs for [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: We consider both a model-match case, in which [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Accuracy of the importance-sampling estimate. We [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Parameter estimates for the memory kernel model. [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

72 extracted references · 66 canonical work pages

  1. [31]

    Boninsegna, F

    L. Boninsegna, F. N¨ uske, and C. Clementi, Sparse learn- ing of stochastic dynamical equations, The Journal of Chemical Physics148(2018)

    work page 2018

  2. [1]

    Brownian motion The MSD for the BM model is m(τ) = 4Dτ,(A3) in two spatial dimensions

    work page

  3. [2]

    Forτ≪γ −1, the velocity remains correlated over the observation interval, so the displacement is approximately proportional toτ and the MSD scales ballistically asτ 2

    Integrated OU process In the stationary state, the MSD of the OU model (2) is given by [46] ˆm(τ) =4D γ3 (e−γτ +γτ−1),(A4) while the V ACF is Cv(τ) = 2D γ e−γτ .(A5) These two quantities show that the OU model contains a single characteristic time scale,γ −1. Forτ≪γ −1, the velocity remains correlated over the observation interval, so the displacement is ...

    work page

  4. [3]

    Mexican-hat model Because of the nonlinear drift term, closed-form MSD and V ACF expressions are not available in the Mexican- hat model (3). Nevertheless, the stationary velocity dis- tribution can be obtained in closed form from the corre- sponding Fokker–Planck equation [18]: ps(v) = 1 C exp − γ 4D ∥v∥4 + γv 2 r 2D ∥v∥2 ,(A6) where the normalization co...

    work page

  5. [4]

    Memory kernel model By introducing an auxiliary variable w := Z t −∞ dt′e−a(t−t′)v(t′),(A9) we can rewrite Eq. (4) as ˙r=v,(A10a) ˙v=−γv+Aw+ √ 2Dξ(t),(A10b) ˙w=−aw+v.(A10c) The stability condition (5) ensures that the origin [(v,w) = (0,0)] is stable for the deterministic part of the subsystem defined by Eqs. (A10b) and (A10c). In the stationary state, th...

    work page

  6. [5]

    ,andC 2 := d2 2 −a 2 d2(d2 2 −d 2

    work page

  7. [6]

    (A11) and (A13) in Supplementary Note 1 of Ref

    (A12b) The MSD in the stationary state is ˆm(τ) = 4D X k=1,2 Ck d2 k e−dkτ +d kτ−1 .(A13) We provide the derivations of Eq. (A11) and (A13) in Supplementary Note 1 of Ref. [36]. Appendix B: Importance sampling with Gaussian mixture proposal

    work page

  8. [7]

    (9) and hence to perform model comparison, we evaluate the marginal likelihood Z := Z dθp(D|θ)p(θ),(B1) 14 which is Eq

    Method To compute the log Bayes factors in Eq. (9) and hence to perform model comparison, we evaluate the marginal likelihood Z := Z dθp(D|θ)p(θ),(B1) 14 which is Eq. (7) written for a fixed candidate model, with the model label and index suppressed. Since this integral is typically not available analytically, we approximate it by importance sampling (IS)...

    work page

Show all 72 references
  1. [8]

    Robustness of importance sampling We first validate the accuracy of the importance- sampling estimator (B3) by comparing it with the “true” marginal likelihood obtained from direct numerical inte- gration of Eq. (7). For numerical convenience, we work with the negative logarit...

  2. [9]

    In other words, we cannot simply replace the unobserved instantaneous ve- locityv i by the secant velocityV i in Eq

    Limitations of secant-velocity approximations When constructing a likelihood for second-order mod- els from position-only observations, a tempting but gen- erally incorrect shortcut is to estimate the velocity by finite differences and substitute it into a likelihood writ- ten...

  3. [10]

    Therefore, for each Cartesian componentα∈ {x, y}, the increment vector ∆r (α) in Eq

    Linear Gaussian models For the linear Gaussian candidates, the positional in- crements remain jointly Gaussian after the latent veloci- ties and auxiliary hidden variables are integrated out [28]. Therefore, for each Cartesian componentα∈ {x, y}, the increment vector ∆r (α) in...

  4. [11]

    We therefore use the transformed-Gaussian approach proposed in Ref

    Nonlinear models For nonlinear models, an exact closed-form increment likelihood is, in general, not available. We therefore use the transformed-Gaussian approach proposed in Ref. [31] to derive the approximate likelihood. Below, we briefly review their approach. Consider a se...

  5. [12]

    E. A. Codling, M. J. Plank, and S. Benhamou, Random walk models in biology, Journal of the Royal Society In- terface5, 813 (2008)

    2008

  6. [13]

    Metzler, J.-H

    R. Metzler, J.-H. Jeon, A. G. Cherstvy, and E. Barkai, Anomalous diffusion models and their properties: non- stationarity, non-ergodicity, and ageing at the centenary of single particle tracking, Physical Chemistry Chemical Physics16, 24128 (2014)

    2014

  7. [14]

    Bechinger, R

    C. Bechinger, R. Di Leonardo, H. L¨ owen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Reviews of Modern Physics88, 045006 (2016)

    2016

  8. [15]

    Selmeczi, L

    D. Selmeczi, L. Li, L. I. Pedersen, S. Nrrelykke, P. H. Hagedorn, S. Mosler, N. B. Larsen, E. C. Cox, and H. Flyvbjerg, Cell motility as random motion: A review, The European Physical Journal Special Topics157, 1 (2008)

    2008

  9. [16]

    I. S. Aranson,Physical models of cell motility(Springer, 2016)

    2016

  10. [17]

    C. H. Stuelten, C. A. Parent, and D. J. Montell, Cell motility in cancer invasion and metastasis: insights from simple model organisms, Nature Reviews Cancer18, 296 (2018)

    2018

  11. [18]

    Kapate, R

    N. Kapate, R. Liao, R. L. Sodemann, T. Stinson, S. Prakash, N. Kumbhojkar, V. C. Suja, L. L.-W. Wang, M. Flanz, R. Rajeev,et al., Backpack-mediated anti- inflammatory macrophage cell therapy for the treat- ment of traumatic brain injury, PNAS Nexus3, pgad434 (2024)

    2024

  12. [19]

    Klages, Cell migration: Beyond Brownian motion, Biophysical Journal123, 1167 (2024)

    R. Klages, Cell migration: Beyond Brownian motion, Biophysical Journal123, 1167 (2024)

    2024

  13. [20]

    D. B. Br¨ uckner and C. P. Broedersz, Learning dynamical models of single and collective cell migration: A review, Reports on Progress in Physics87, 056601 (2024)

    2024

  14. [21]

    M. H. Gail and C. W. Boone, The locomotion of mouse fibroblasts in tissue culture, Biophysical Journal10, 980 (1970)

    1970

  15. [22]

    G. E. Uhlenbeck and L. S. Ornstein, On the theory of the Brownian motion, Physical Review36, 823 (1930)

    1930

  16. [23]

    Selmeczi, S

    D. Selmeczi, S. Mosler, P. H. Hagedorn, N. B. Larsen, and H. Flyvbjerg, Cell motility as persistent random motion: Theories from experiments, Biophysical Journal89, 912 (2005)

    2005

  17. [24]

    Takagi, M

    H. Takagi, M. J. Sato, T. Yanagida, and M. Ueda, Func- tional analysis of spontaneous cell movement under dif- ferent physiological conditions, PloS One3, e2648 (2008)

    2008

  18. [25]

    B. G. Mitterwallner, C. Schreiber, J. O. Daldrop, J. O. R¨ adler, and R. R. Netz, Non-Markovian data-driven modeling of single-cell motility, Physical Review E101, 032408 (2020)

    2020

  19. [26]

    Campos, V

    D. Campos, V. M´ endez, and I. Llopis, Persistent random motion: Uncovering cell migration dynamics, Journal of Theoretical Biology267, 526 (2010)

    2010

  20. [27]

    L. Li, E. C. Cox, and H. Flyvbjerg, ‘Dicty dynam- ics’: Dictyostelium motility as persistent random motion, Physical Biology8, 046006 (2011)

    2011

  21. [28]

    L. Li, S. F. Nørrelykke, and E. C. Cox, Persistent cell mo- tion in the absence of external signals: A search strategy for eukaryotic cells, PLoS One3, e2093 (2008)

    2008

  22. [29]

    Erdmann, W

    U. Erdmann, W. Ebeling, L. Schimansky-Geier, and F. Schweitzer, Brownian particles far from equilibrium, The European Physical Journal B-Condensed Matter and Complex Systems15, 105 (2000)

    2000

  23. [30]

    Romanczuk, M

    P. Romanczuk, M. B¨ ar, W. Ebeling, B. Lindner, and L. Schimansky-Geier, Active Brownian particles: From individual to collective stochastic dynamics, The Euro- pean Physical Journal Special Topics202, 1 (2012)

    2012

  24. [32]

    D. B. Br¨ uckner, P. Ronceray, and C. P. Broedersz, Infer- ring the dynamics of underdamped stochastic systems, Physical Review Letters125, 058103 (2020)

    2020

  25. [33]

    Frishman and P

    A. Frishman and P. Ronceray, Learning force fields from stochastic trajectories, Physical Review X10, 021009 (2020)

    2020

  26. [34]

    M. R. R. Tabar, F. Nikakhtar, L. Parkavousi, A. Akhshi, U. Feudel, and K. Lehnertz, Revealing higher-order in- teractions in high-dimensional complex systems: A data- driven approach, Physical Review X14, 011050 (2024)

    2024

  27. [35]

    D. B. Br¨ uckner, A. Fink, C. Schreiber, P. J. R¨ ottgermann, J. O. R¨ adler, and C. P. Broedersz, Stochastic nonlinear dynamics of confined cell migration in two-state systems, Nature Physics15, 595 (2019)

    2019

  28. [36]

    Gerardos and P

    A. Gerardos and P. Ronceray, Principled model selection for stochastic dynamics, Physical Review Letters135, 167401 (2025)

    2025

  29. [37]

    Kashiwamura, Y

    S. Kashiwamura, Y. Kato, H. Kori, and M. Okada, Uncertainty-aware sparse identification of dynamical sys- tems via Bayesian model averaging, arXiv preprint arXiv:2604.10854 (2026)

    2026 arXiv

  30. [38]

    E. A. Ferguson, J. Matthiopoulos, R. H. Insall, and D. Husmeier, Inference of the drivers of collective move- ment in two cell types: Dictyostelium and melanoma, Journal of The Royal Society Interface13(2016)

    2016

  31. [39]

    M. Lysy, N. S. Pillai, D. B. Hill, M. G. Forest, J. W. Mellnik, P. A. Vasquez, and S. A. McKinley, Model com- parison and assessment for single particle tracking in bi- ological fluids, Journal of the American Statistical Asso- ciation111, 1413 (2016)

    2016

  32. [40]

    Thapa, M

    S. Thapa, M. A. Lomholt, J. Krog, A. G. Cher- stvy, and R. Metzler, Bayesian analysis of single- particle tracking data using the nested-sampling algo- rithm: maximum-likelihood model selection applied to stochastic-diffusivity data, Physical Chemistry Chemical Physics20, 29018 (2018)

    2018

  33. [41]

    M. T. Brolly, J. R. Maddison, A. L. Teckentrup, and J. Vanneste, Bayesian comparison of stochastic models of dispersion, Journal of Fluid Mechanics944, A2 (2022)

    2022

  34. [42]

    Albrecht, M

    J. Albrecht, M. Opper, and R. Großmann, A likelihood approach for inference of population heterogeneity in par- ticle ensembles with second-order Langevin dynamics, Communications Physics9(2026)

    2026

  35. [43]

    C. M. Bishop,Pattern recognition and machine learning, Information science and statistics (Springer, New York, 2006)

    2006

  36. [44]

    Von Toussaint, Bayesian inference in physics, Reviews of Modern Physics83, 943 (2011)

    U. Von Toussaint, Bayesian inference in physics, Reviews of Modern Physics83, 943 (2011)

    2011

  37. [45]

    Jeffreys,The theory of probability(OuP Oxford, 1998)

    H. Jeffreys,The theory of probability(OuP Oxford, 1998)

    1998

  38. [46]

    Llorente, L

    F. Llorente, L. Martino, E. Curbelo, J. L´ opez-Santiago, and D. Delgado, On the safe use of prior densities for bayesian model selection, Wiley Interdisciplinary Re- 19 views: Computational Statistics15, e1595 (2023)

    2023

  39. [47]

    See Supplementary Information for this manuscript

  40. [48]

    Bloomfield, Y

    G. Bloomfield, Y. Tanaka, J. Skelton, A. Ivens, and R. R. Kay, Widespread duplications in the genomes of labora- tory stocks ofDictyostelium discoideum, Genome Biology 9, R75 (2008)

    2008

  41. [49]

    Großmann, L

    R. Großmann, L. S. Bort, T. Moldenhawer, M. Stange, S. S. Panah, R. Metzler, and C. Beta, Non-Gaussian dis- placements in active transport on a carpet of motile cells, Physical Review Letters132, 088301 (2024)

    2024

  42. [50]

    Albrecht, L

    J. Albrecht, L. S. Dautzenberg, M. Opper, C. Beta, and R. Großmann, Likelihood-based heterogeneity infer- ence reveals nonstationary effects in biohybrid cell-cargo transport, Physical Review Research8, 013106 (2026)

    2026

  43. [51]

    Martino, V

    L. Martino, V. Elvira, and F. Louzada, Effective sam- ple size for importance sampling based on discrepancy measures, Signal Processing131, 386 (2017)

    2017

  44. [52]

    Elvira, L

    V. Elvira, L. Martino, and C. P. Robert, Rethinking the effective sample size, International Statistical Review90, 525 (2022)

    2022

  45. [53]

    Hukushima and K

    K. Hukushima and K. Nemoto, Exchange Monte Carlo method and application to spin glass simulations, Journal of the Physical Society of Japan65, 1604 (1996)

    1996

  46. [54]

    Nagata, S

    K. Nagata, S. Sugita, and M. Okada, Bayesian spectral deconvolution with the exchange Monte Carlo method, Neural Networks28, 82 (2012)

    2012

  47. [55]

    Y. Kato, S. Kashiwamura, E. Watanabe, M. Okada, and H. Kori, Bayesian estimation of coupling strength and heterogeneity in a coupled oscillator model from macro- scopic quantities, Physical Review E112, 034215 (2025). [45]https://github.com/yuu-kato/motility_comparison

    2025

  48. [56]

    Ebeling and I

    W. Ebeling and I. Sokolov,Statistical thermodynamics and stochastic theory of nonequilibrium systems, Vol. 8 (World Scientific Publishing Company, 2005)

    2005

  49. [57]

    Owen and Y

    A. Owen and Y. Zhou, Safe and effective importance sam- pling, Journal of the American Statistical Association95, 135 (2000)

    2000

  50. [58]

    Elvira, L

    V. Elvira, L. Martino, D. Luengo, and M. F. Bugallo, Heretical multiple importance sampling, IEEE Signal Processing Letters23, 1474 (2016)

    2016

  51. [59]

    Elvira, L

    V. Elvira, L. Martino, D. Luengo, and M. F. Bugallo, Generalized multiple importance sampling, Statistical Science34, 129 (2019)

    2019

  52. [60]

    Hesterberg, Weighted average importance sampling and defensive mixture distributions, Technometrics37, 185 (1995)

    T. Hesterberg, Weighted average importance sampling and defensive mixture distributions, Technometrics37, 185 (1995)

    1995

  53. [61]

    Kong, A note on importance sampling using standard- ized weights, University of Chicago, Dept

    A. Kong, A note on importance sampling using standard- ized weights, University of Chicago, Dept. of Statistics, Tech. Rep348, 14 (1992)

    1992

  54. [62]

    A. Kong, J. S. Liu, and W. H. Wong, Sequential impu- tations and Bayesian missing data problems, Journal of the American statistical association89, 278 (1994)

    1994

  55. [63]

    J. S. Liu,Monte Carlo strategies in scientific computing, Vol. 10 (Springer, 2001)

    2001

  56. [64]

    Blanchard, D

    P. Blanchard, D. J. Higham, and N. J. Higham, Accu- rately computing the log-sum-exp and softmax functions, IMA Journal of Numerical Analysis41, 2311 (2021)

    2021

  57. [65]

    Hcubature.jl,https://github.com/JuliaMath/ HCubature.jl

  58. [66]

    A. C. Genz and A. A. Malik, Remarks on algorithm 006: An adaptive algorithm for numerical integration over an N-dimensional rectangular region, Journal of Computa- tional and Applied mathematics6, 295 (1980)

    1980

  59. [67]

    Ferretti, V

    F. Ferretti, V. Chardes, T. Mora, A. M. Walczak, and I. Giardina, Building general langevin models from dis- crete datasets, Physical Review X10, 031018 (2020)

    2020

  60. [68]

    Bayesian comparison of Langevin dynamics for cell motility from positional observation

    F. Ferretti, V. Chard` es, T. Mora, A. M. Walczak, and I. Giardina, Renormalization group approach to con- nect discrete-and continuous-time descriptions of Gaus- sian processes, Physical Review E105, 044133 (2022). Supplementary Information for “Bayesian comparison of Langevi...

    2022

  61. [69]

    A. H. Sayed and T. Kailath, A survey of spectral factorization methods, Numerical Linear Algebra with Applications8, 467 (2001)

    2001

  62. [70]

    Serre,Matrices: Theory and Applications, 2nd ed

    D. Serre,Matrices: Theory and Applications, 2nd ed. (Springer, New York, NY, 2010)

    2010

  63. [71]

    Optim.jl,https://github.com/JuliaNLSolvers/Optim.jl

  64. [72]

    I. M. Sobol, Distribution of points in a cube and approximate evaluation of integrals, USSR Computational Mathematics and Mathematical Physics7, 86 (1967)

    1967

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.