pith. sign in

arxiv: 2605.17868 · v1 · pith:5OQ4JCUAnew · submitted 2026-05-18 · ⚛️ nucl-th · hep-ph· nucl-ex

Sequential Bayesian inference with correlated heavy-ion datasets

Lipei Du This is my paper

Pith reviewed 2026-05-20 01:05 UTC · model grok-4.3

classification ⚛️ nucl-th hep-phnucl-ex
keywords Bayesian inferencesequential updatingheavy-ion collisionscorrelated datasetsconditional likelihoodinformation decompositionposterior biaspseudo-data
0
0 comments X

The pith

Factorized sequential Bayesian updates on correlated heavy-ion datasets produce systematic posterior deviations that grow with correlation strength.

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

The paper demonstrates that treating statistically correlated datasets as independent when updating posteriors sequentially leads to inconsistent results compared to a joint analysis. In a controlled study with pseudo-data, the authors show that these deviations arise because factorized updates ignore shared information, while using the exact conditional likelihood keeps the sequential result identical to the joint one. They introduce an information decomposition to separate new information from redundant information across datasets and trace how correlations redistribute this information in a way that depends on the model parameters. This matters for heavy-ion physics because many experimental observables share common uncertainties from the same collision events or detector effects. The work supplies a diagnostic to check when sequential inference remains reliable and when a joint treatment is required.

Core claim

In a controlled setting using pseudo-data with a tunable covariance structure, factorized sequential updates reproduce the joint posterior only in the limit of conditional independence; otherwise they produce systematic deviations that increase with correlation strength. Conditional updates based on the exact conditional likelihood remain fully consistent with the joint inference result. An information decomposition separates contributions into new and redundant components across datasets, revealing that correlations induce a structured, parameter-dependent redistribution of information governed by the overlap of dataset sensitivities.

What carries the argument

The tunable covariance structure imposed on pseudo-data together with the information decomposition that isolates parameter-dependent new versus redundant information contributions.

If this is right

  • Sequential Bayesian analyses of heavy-ion data must switch to conditional likelihood updates whenever measurable correlations exist between datasets.
  • The magnitude of posterior bias scales directly with the strength of inter-dataset correlations.
  • The introduced information decomposition can serve as a practical diagnostic to flag inconsistent sequential updates.
  • A fully consistent treatment requires embedding all datasets inside a single probabilistic model that accounts for their joint covariance.

Where Pith is reading between the lines

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

  • Existing published posteriors from staged heavy-ion analyses may shift once correlations are properly included.
  • The same controlled pseudo-data test can be applied to other fields that perform sequential inference on correlated observables, such as cosmology or particle physics.
  • Approximate schemes that capture the leading correlation effects without full joint sampling could be developed for computationally expensive models.

Load-bearing premise

The imposed covariance structure on the pseudo-data accurately represents the statistical correlations present in actual heavy-ion collision measurements.

What would settle it

Perform a joint versus factorized sequential inference on real heavy-ion datasets with independently estimated correlations and measure whether the posterior shift matches the size predicted by the correlation strength.

Figures

Figures reproduced from arXiv: 2605.17868 by Lipei Du.

Figure 1
Figure 1. Figure 1: Correlation matrices for the pseudo-data at two representative [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Data-space information flow I2←1 as a function of the correlation strength ρ. (b) Corresponding parameter-resolved redundancy measure ri for selected values of ρ. as derived explicitly in Appendix B, showing that the response of D2 is reduced by the component that can be predicted from D1. The conditional Fisher matrix then becomes F2|1 = J T 2|1Σ −1 2|1 J2|1, (16) which quantifies the genuinely new in… view at source ↗
Figure 4
Figure 4. Figure 4: Posterior contours for joint inference (black solid), factorized se [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Kullback–Leibler (KL) divergence between sequential posteriors [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

Bayesian inference provides a natural framework for updating knowledge as new information becomes available, often in a sequential manner by incorporating datasets in stages or reusing previous posteriors as priors. In practice, this is commonly implemented using a factorized update in which datasets are treated as conditionally independent. When datasets are statistically correlated, however, this approximation becomes inconsistent with the joint likelihood and can lead to biased posterior estimates. In this work, we investigate this issue in a controlled setting using pseudo-data with a tunable covariance structure. We compare joint inference, factorized sequential updating, and a formulation based on the exact conditional likelihood. We show that factorized updates reproduce the joint posterior only in the limit of conditional independence, and otherwise lead to systematic deviations that grow with the correlation strength, while conditional updates remain consistent with the joint result. To interpret these deviations, we introduce an information decomposition that separates contributions into components that are new and components that are redundant across datasets. We show that correlations induce a structured, parameter-dependent redistribution of information, governed by the overlap of dataset sensitivities. The resulting mismatch between marginal and conditional information quantitatively explains the observed deviations. These results provide a practical diagnostic for assessing the consistency of sequential Bayesian inference with correlated datasets and highlight the need for a consistent treatment of correlations within a common probabilistic framework.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a controlled numerical experiment using pseudo-data with a tunable covariance structure to compare three Bayesian inference approaches for heavy-ion collision observables: full joint inference, factorized sequential updates (assuming conditional independence), and updates based on the exact conditional likelihood. It reports that factorized updates match the joint posterior only in the limit of zero correlation and otherwise produce systematic deviations that increase with correlation strength, while conditional updates remain consistent with the joint result. An information decomposition is introduced to separate new versus redundant information contributions across datasets and to attribute the observed mismatches to parameter-dependent overlaps in dataset sensitivities.

Significance. If the central numerical trends hold, the work supplies a concrete diagnostic for when sequential Bayesian updating remains reliable in the presence of correlated heavy-ion datasets, a common situation in the field. The controlled pseudo-data setup with explicit variation of correlation strength isolates the effect cleanly and yields clear, reproducible trends. Credit is due for the direct comparison against the joint reference posterior and for framing the information decomposition as an interpretive rather than self-referential tool. The results underscore the practical need for consistent probabilistic treatment of correlations rather than ad-hoc factorized updates.

major comments (2)
  1. [Abstract / methods (information decomposition)] Abstract and methods section on the information decomposition: the claim that the decomposition 'quantitatively explains the observed deviations' rests on the separation into new and redundant components being independent of the posterior mismatch it is used to explain. A short derivation or explicit numerical check confirming that the redundant term exactly accounts for the factorized-versus-joint difference (rather than being fitted to it) would remove any appearance of circularity and strengthen the interpretive claim.
  2. [Pseudo-data generation] Pseudo-data generation paragraph: the tunable covariance model is central to the reported trends with correlation strength, yet the manuscript does not appear to test whether the chosen functional form of the covariance (or the range of the correlation-strength parameter) produces qualitatively similar deviations when replaced by a covariance estimated from actual heavy-ion experimental uncertainties. This test is load-bearing for the practical-diagnostic conclusion.
minor comments (2)
  1. [Figures] Figure captions should explicitly state the correlation-strength values used in each panel and whether the plotted posteriors are marginal or joint.
  2. [Notation] The notation for the correlation strength parameter and for the information components (new/redundant) should be introduced once in the main text with a clear equation reference rather than only in the abstract.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful review and the recommendation for minor revision. We are pleased that the significance of the controlled experiment and the information decomposition is recognized. Below we respond to each major comment.

read point-by-point responses

  1. Referee: [Abstract / methods (information decomposition)] Abstract and methods section on the information decomposition: the claim that the decomposition 'quantitatively explains the observed deviations' rests on the separation into new and redundant components being independent of the posterior mismatch it is used to explain. A short derivation or explicit numerical check confirming that the redundant term exactly accounts for the factorized-versus-joint difference (rather than being fitted to it) would remove any appearance of circularity and strengthen the interpretive claim.

    Authors: We thank the referee for highlighting this point. The information decomposition is derived from the mutual information between parameters and datasets, with the redundant component defined via the intersection of information contents, which is computed directly from the sensitivities without reference to the posterior mismatch. In the revised version, we will add a concise derivation in the methods section demonstrating this independence, along with a numerical check where we compute the mismatch directly and verify that it matches the redundant information term for various correlation strengths. This will confirm that the explanation is not circular. revision: yes

  2. Referee: [Pseudo-data generation] Pseudo-data generation paragraph: the tunable covariance model is central to the reported trends with correlation strength, yet the manuscript does not appear to test whether the chosen functional form of the covariance (or the range of the correlation-strength parameter) produces qualitatively similar deviations when replaced by a covariance estimated from actual heavy-ion experimental uncertainties. This test is load-bearing for the practical-diagnostic conclusion.

    Authors: We agree that connecting to real experimental covariances would be valuable for broader applicability. However, the primary goal of this work is to isolate the effect of correlations in a controlled manner by varying the strength parameter systematically. The chosen functional form is a standard Gaussian process-like covariance that allows continuous tuning from independent to fully correlated cases, enabling clear identification of trends. We will revise the pseudo-data section to include a more detailed justification of this model choice, explaining how it captures essential features such as shared systematic uncertainties common in heavy-ion observables. A full test with real data covariances is an important direction for follow-up studies but would require additional datasets and is beyond the scope of the current controlled experiment. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The manuscript conducts a controlled numerical comparison of joint, factorized, and conditional Bayesian updates on pseudo-data generated with an explicit tunable covariance model. All central results follow from direct posterior sampling and a newly introduced information decomposition presented as an interpretive tool; no equation or claim reduces by construction to a fitted quantity defined from the same data, and no load-bearing premise rests on self-citation chains or imported uniqueness theorems. The derivation chain remains self-contained within the stated probabilistic framework and external benchmarks of consistency.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on the ability to generate pseudo-data whose covariance can be dialed independently of the model parameters, on standard Bayesian updating rules, and on the validity of the newly introduced information decomposition for interpreting deviations. No machine-checked proofs or external benchmarks are mentioned.

free parameters (1)
  • correlation strength parameter
    Tunable scalar that controls the off-diagonal elements of the covariance matrix in the pseudo-data generation; directly varied to demonstrate growth of deviations.
axioms (2)
  • domain assumption Pseudo-data generated with an imposed covariance matrix accurately represents the statistical correlations that exist among real heavy-ion observables
    Invoked to create the controlled setting in which joint, factorized, and conditional posteriors can be compared.
  • ad hoc to paper The information decomposition into new versus redundant components is a valid separation that quantitatively accounts for the observed posterior mismatch
    Introduced in the abstract to interpret why factorized updates deviate; its correctness is not independently verified outside the numerical experiment.
invented entities (1)
  • information decomposition no independent evidence
    purpose: Separates the total information contributed by each dataset into components that are new versus redundant with respect to previous datasets
    Postulated to explain the structured, parameter-dependent redistribution of information induced by correlations.

pith-pipeline@v0.9.0 · 5748 in / 1745 out tokens · 60661 ms · 2026-05-20T01:05:27.735090+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

45 extracted references · 45 canonical work pages · 13 internal anchors

  1. [1]

    Bayes in the sky: Bayesian inference and model selection in cosmology

    R. Trotta, Bayes in the sky: Bayesian inference and model selection in cosmology, Contemp. Phys. 49 (2008) 71–104. arXiv:0803.4089, doi:10.1080/00107510802066753

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1080/00107510802066753 2008

  2. [2]

    MacKay, Information Theory, Inference and Learning Algorithms, Cambridge University Press, 2003

    D. MacKay, Information Theory, Inference and Learning Algorithms, Cambridge University Press, 2003. URL https://books.google.com/books?id=AKuMj4PN_EMC

    work page 2003

  3. [3]

    A. R. Liddle, Statistical methods for cosmological parameter selection and estimation, Ann. Rev. Nucl. Part. Sci. 59 (2009) 95–114. arXiv: 0903.4210, doi:10.1146/annurev.nucl.010909.083706

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1146/annurev.nucl.010909.083706 2009

  4. [4]

    Constraining the Eq. of State of Super-Hadronic Matter from Heavy-Ion Collisions

    S. Pratt, E. Sangaline, P. Sorensen, H. Wang, Constraining the Eq. of State of Super-Hadronic Matter from Heavy-Ion Collisions, Phys. Rev. Lett. 114 (2015) 202301. arXiv:1501.04042, doi:10.1103/ PhysRevLett.114.202301

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  5. [5]

    J. E. Bernhard, J. S. Moreland, S. A. Bass, J. Liu, U. Heinz, Applying Bayesian parameter estimation to relativistic heavy-ion collisions: si- multaneous characterization of the initial state and quark-gluon plasma medium, Phys. Rev. C 94 (2) (2016) 024907. arXiv:1605.03954, doi:10.1103/PhysRevC.94.024907

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.94.024907 2016

  6. [6]

    J. E. Bernhard, J. S. Moreland, S. A. Bass, Bayesian estimation of the specific shear and bulk viscosity of quark–gluon plasma, Nature Phys. 15 (11) (2019) 1113–1117. doi:10.1038/s41567-019-0611-8

    work page doi:10.1038/s41567-019-0611-8 2019

  7. [7]

    G. Nijs, W. van der Schee, U. G ¨ursoy, R. Snellings, Transverse Momen- tum Di fferential Global Analysis of Heavy-Ion Collisions, Phys. Rev. Lett. 126 (20) (2021) 202301. arXiv:2010.15130, doi:10.1103/ PhysRevLett.126.202301

    work page arXiv 2021

  8. [8]

    G. Nijs, W. van der Schee, U. G ¨ursoy, R. Snellings, Bayesian analy- sis of heavy ion collisions with the heavy ion computational framework Trajectum, Phys. Rev. C 103 (5) (2021) 054909. arXiv:2010.15134, doi:10.1103/PhysRevC.103.054909

    work page doi:10.1103/physrevc.103.054909 2021

  9. [9]

    Everett et al

    D. Everett, et al., Phenomenological constraints on the transport prop- erties of QCD matter with data-driven model averaging, Phys. Rev. Lett. 126 (24) (2021) 242301. arXiv:2010.03928, doi:10.1103/ PhysRevLett.126.242301

    work page arXiv 2021

  10. [10]

    Everett, et al., Multisystem Bayesian constraints on the transport co- efficients of QCD matter, Phys

    D. Everett, et al., Multisystem Bayesian constraints on the transport co- efficients of QCD matter, Phys. Rev. C 103 (5) (2021) 054904. arXiv: 2011.01430, doi:10.1103/PhysRevC.103.054904

    work page doi:10.1103/physrevc.103.054904 2021

  11. [11]

    Fan, et al., New metric improving Bayesian calibration of a mul- tistage approach studying hadron and inclusive jet suppression, Phys

    W. Fan, et al., New metric improving Bayesian calibration of a mul- tistage approach studying hadron and inclusive jet suppression, Phys. Rev. C 109 (6) (2024) 064903. arXiv:2307.09641, doi:10.1103/ PhysRevC.109.064903

    work page arXiv 2024

  12. [12]

    Cao, et al., Determining the jet transport coe fficient ˆq from inclusive hadron suppression measurements using Bayesian parameter estimation, Phys

    S. Cao, et al., Determining the jet transport coe fficient ˆq from inclusive hadron suppression measurements using Bayesian parameter estimation, Phys. Rev. C 104 (2) (2021) 024905. arXiv:2102.11337, doi:10. 1103/PhysRevC.104.024905

    work page arXiv 2021

  13. [14]

    Mankolli, et al., Longitudinal Dynamics of Large and Small Sys- tems from a 3D Bayesian Calibration of RHIC Top-energy Collision DataarXiv:2601.17234

    A. Mankolli, et al., Longitudinal Dynamics of Large and Small Sys- tems from a 3D Bayesian Calibration of RHIC Top-energy Collision DataarXiv:2601.17234

    work page arXiv

  14. [15]

    Du, Multi-observable analysis of jet quenching using Bayesian in- ference with JETSCAPE, Nucl

    L. Du, Multi-observable analysis of jet quenching using Bayesian in- ference with JETSCAPE, Nucl. Phys. A 1060 (2025) 123100. doi: 10.1016/j.nuclphysa.2025.123100. 10

    work page doi:10.1016/j.nuclphysa.2025.123100 2025

  15. [16]

    D. S. Sivia, Data analysis : a Bayesian tutorial, second edition. Edition, Oxford science publications, Clarendon, Oxford, 2006

    work page 2006

  16. [17]

    Bayesian inference in physics

    U. von Toussaint, Bayesian inference in physics, Rev. Mod. Phys. 83 (2011) 943–999. doi:10.1103/RevModPhys.83.943

    work page doi:10.1103/revmodphys.83.943 2011

  17. [18]

    Paquet, Applications of emulation and Bayesian methods in heavy- ion physics, J

    J.-F. Paquet, Applications of emulation and Bayesian methods in heavy- ion physics, J. Phys. G 51 (10) (2024) 103001. arXiv:2310.17618, doi:10.1088/1361-6471/ad6a2b

    work page doi:10.1088/1361-6471/ad6a2b 2024

  18. [19]

    Bishop, Pattern Recognition and Machine Learning, Information Sci- ence and Statistics, Springer, 2006

    C. Bishop, Pattern Recognition and Machine Learning, Information Sci- ence and Statistics, Springer, 2006. URL https://books.google.de/books?id=qWPwnQEACAAJ

    work page 2006

  19. [20]

    Van de Schoot, S

    R. Van de Schoot, S. Depaoli, R. King, B. Kramer, K. M ¨artens, M. G. Tadesse, M. Vannucci, A. Gelman, D. Veen, J. Willemsen, et al., Bayesian statistics and modelling, Nature Reviews Methods Primers 1 (1) (2021) 1

    work page 2021

  20. [21]

    H. Roch, C. Shen, Learning informed prior distributions with normalizing flows for Bayesian analysis, Phys. Rev. C 113 (3) (2026) 034903.arXiv: 2509.14911, doi:10.1103/wms4-m4cb

    work page doi:10.1103/wms4-m4cb 2026

  21. [22]

    Transverse momentum-flow correlations in relativistic heavy-ion collisions

    P. Bozek, Transverse-momentum–flow correlations in relativistic heavy- ion collisions, Phys. Rev. C 93 (4) (2016) 044908. arXiv:1601.04513, doi:10.1103/PhysRevC.93.044908

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.93.044908 2016

  22. [23]

    Extracting the shear viscosity of the quark-gluon plasma from flow in ultra-central heavy-ion collisions

    M. Luzum, J.-Y . Ollitrault, Extracting the shear viscosity of the quark- gluon plasma from flow in ultra-central heavy-ion collisions, Nucl. Phys. A 904-905 (2013) 377c–380c. arXiv:1210.6010, doi:10.1016/j. nuclphysa.2013.02.028

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j 2013

  23. [24]

    Ollitrault, Anisotropy as a signature of transverse collective flow, Phys

    J.-Y . Ollitrault, Anisotropy as a signature of transverse collective flow, Phys. Rev. D 46 (1992) 229–245. doi:10.1103/PhysRevD.46.229

    work page doi:10.1103/physrevd.46.229 1992

  24. [25]

    L. Du, H. Gao, S. Jeon, C. Gale, Rapidity scan with multistage hydrody- namic and statistical thermal models, Phys. Rev. C 109 (1) (2024) 014907. arXiv:2302.13852, doi:10.1103/PhysRevC.109.014907

    work page doi:10.1103/physrevc.109.014907 2024

  25. [26]

    Triangularity and Dipole Asymmetry in Heavy Ion Collisions

    D. Teaney, L. Yan, Triangularity and Dipole Asymmetry in Heavy Ion Collisions, Phys. Rev. C 83 (2011) 064904. arXiv:1010.1876, doi: 10.1103/PhysRevC.83.064904

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.83.064904 2011

  26. [27]

    Du, Kinematic and dynamical origins of mean-pT fluctuations in heavy-ion collisions, Phys

    L. Du, Kinematic and dynamical origins of mean-pT fluctuations in heavy-ion collisions, Phys. Lett. B 874 (2026) 140225. arXiv:2512. 22715, doi:10.1016/j.physletb.2026.140225

    work page doi:10.1016/j.physletb.2026.140225 2026

  27. [28]

    J. S. Moreland, J. E. Bernhard, S. A. Bass, Bayesian calibration of a hy- brid nuclear collision model using p-Pb and Pb-Pb data at energies avail- able at the CERN Large Hadron Collider, Phys. Rev. C 101 (2) (2020) 024911. arXiv:1808.02106, doi:10.1103/PhysRevC.101.024911

    work page doi:10.1103/physrevc.101.024911 2020

  28. [29]

    Du, Advancing multimessenger approaches in heavy-ion collisions: Insights from electromagnetic probes, EPJ Web Conf

    L. Du, Advancing multimessenger approaches in heavy-ion collisions: Insights from electromagnetic probes, EPJ Web Conf. 339 (2025) 01016. arXiv:2503.09045, doi:10.1051/epjconf/202533901016

    work page doi:10.1051/epjconf/202533901016 2025

  29. [30]

    Sorensen, et al., Dense nuclear matter equation of state from heavy- ion collisions, Prog

    A. Sorensen, et al., Dense nuclear matter equation of state from heavy- ion collisions, Prog. Part. Nucl. Phys. 134 (2024) 104080. arXiv:2301. 13253, doi:10.1016/j.ppnp.2023.104080

    work page doi:10.1016/j.ppnp.2023.104080 2024

  30. [31]

    L. Du, U. Heinz, Electromagnetic Tomography of Radial Flow in the Quark-Gluon Plasma, Phys. Rev. Lett. 136 (10) (2026) 102301. arXiv: 2505.20752, doi:10.1103/ptyq-cs9m

    work page doi:10.1103/ptyq-cs9m 2026

  31. [32]

    Arslandok et al., (2023), arXiv:2303.17254 [nucl-ex]

    M. Arslandok, et al., Hot QCD White Paper arXiv:2303.17254

    work page arXiv

  32. [33]

    L. Du, A. Sorensen, M. Stephanov, The QCD phase diagram and Beam Energy Scan physics: A theory overview, Int. J. Mod. Phys. E 33 (07) (2024) 2430008. arXiv:2402.10183, doi:10.1142/ 9789811294679_0007

    work page arXiv 2024

  33. [34]

    Yamauchi, L

    Y . Yamauchi, L. Buskirk, P. Giuliani, K. Godbey, Normalizing Flows for Bayesian Posteriors: Reproducibility and Deployment arXiv:2310. 04635

    work page

  34. [35]

    R. A. Soltz, D. A. Hangal, A. Angerami, Simple model to investigate jet quenching and correlated errors for centrality-dependent nuclear modi- fication factors in relativistic heavy-ion collisions, Phys. Rev. C 111 (3) (2025) 034911. arXiv:2412.03724, doi:10.1103/PhysRevC.111. 034911

    work page doi:10.1103/physrevc.111 2025

  35. [36]

    Collective flow and viscosity in relativistic heavy-ion collisions

    U. Heinz, R. Snellings, Collective flow and viscosity in relativistic heavy- ion collisions, Ann. Rev. Nucl. Part. Sci. 63 (2013) 123–151. arXiv: 1301.2826, doi:10.1146/annurev-nucl-102212-170540

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1146/annurev-nucl-102212-170540 2013

  36. [37]

    Giacalone, A

    G. Giacalone, A. Mazeliauskas, S. Schlichting, Hydrodynamic attractors, initial state energy and particle production in relativistic nuclear colli- sions, Phys. Rev. Lett. 123 (26) (2019) 262301. arXiv:1908.02866, doi:10.1103/PhysRevLett.123.262301

    work page doi:10.1103/physrevlett.123.262301 2019

  37. [38]

    L. Du, C. Shen, S. Jeon, C. Gale, Probing initial baryon stopping and equation of state with rapidity-dependent directed flow of identified par- ticles, Phys. Rev. C 108 (4) (2023) L041901. arXiv:2211.16408, doi:10.1103/PhysRevC.108.L041901

    work page doi:10.1103/physrevc.108.l041901 2023

  38. [39]

    Du, Bulk medium properties of heavy-ion collisions from the beam energy scan with a multistage hydrodynamic model, Phys

    L. Du, Bulk medium properties of heavy-ion collisions from the beam energy scan with a multistage hydrodynamic model, Phys. Rev. C 110 (1) (2024) 014904. arXiv:2401.00596, doi:10.1103/PhysRevC.110. 014904

    work page doi:10.1103/physrevc.110 2024

  39. [40]

    Collision geometry fluctuations and triangular flow in heavy-ion collisions

    B. Alver, G. Roland, Collision geometry fluctuations and triangular flow in heavy-ion collisions, Phys. Rev. C 81 (2010) 054905, [Erratum: Phys.Rev.C 82, 039903 (2010)]. arXiv:1003.0194, doi:10.1103/ PhysRevC.82.039903

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  40. [41]

    F. G. Gardim, F. Grassi, M. Luzum, J.-Y . Ollitrault, Mapping the hydrody- namic response to the initial geometry in heavy-ion collisions, Phys. Rev. C 85 (2012) 024908. arXiv:1111.6538, doi:10.1103/PhysRevC. 85.024908

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc 2012

  41. [42]

    Centrality dependence of the charged-particle multiplicity density at mid-rapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV

    K. Aamodt, et al., Centrality dependence of the charged-particle mul- tiplicity density at mid-rapidity in Pb-Pb collisions at √sNN = 2.76 TeV, Phys. Rev. Lett. 106 (2011) 032301. arXiv:1012.1657, doi: 10.1103/PhysRevLett.106.032301

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.106.032301 2011

  42. [43]

    Higher harmonic anisotropic flow measurements of charged particles in Pb-Pb collisions at 2.76 TeV

    K. Aamodt, et al., Higher harmonic anisotropic flow measurements of charged particles in Pb-Pb collisions at √sNN =2.76 TeV, Phys. Rev. Lett. 107 (2011) 032301. arXiv:1105.3865, doi:10.1103/PhysRevLett. 107.032301

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett 2011

  43. [44]

    C. E. Rasmussen, C. K. I. Williams, Gaussian Processes for Machine Learning, The MIT Press, 2005. doi:10.7551/mitpress/3206.001. 0001

    work page doi:10.7551/mitpress/3206.001 2005

  44. [45]

    Kullback, R

    S. Kullback, R. A. Leibler, On information and su fficiency, The annals of mathematical statistics 22 (1) (1951) 79–86

    work page 1951

  45. [46]

    J. H. Putschke, et al., The JETSCAPE framework arXiv:1903.07706. 11

    work page internal anchor Pith review Pith/arXiv arXiv 1903