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Bayesian Analysis of Non-extensive Parameters in Au-Au Collisions

Randy Dobler, Juliana O. Costa, Marcelo D. Alloy, Débora P. Menezes

TL;DR

This work addresses hadronization in relativistic heavy-ion collisions by applying a Bayesian NES framework to estimate $q$, $T$, and $μ$ from particle-yield ratios and by comparing NES to an EV-HRG model using Bayes factors. It formalizes a three-parameter inferential setup with uniform priors, uses an affine-invariant MCMC ensemble to sample the posterior, and examines computational choices via diagnostic plots. The study finds robust parameter estimates (e.g., $q≈1.16$, $T≈59$ MeV, $μ≈52$ MeV) and shows that the Bayes factor does not decisively favor NES over EV-HRG, highlighting the value and limitations of Bayesian model comparison in this context. Overall, the combination of NES with Bayesian inference provides a reproducible and uncertainty-aware framework for modeling particle distributions in Au-Au collisions and suggests avenues for future refinements in relativistic nuclear interaction studies.

Abstract

In this work, a Bayesian statistical framework is employed to analyze particle yield ratios in Au-Au collisions, utilizing Non-Extensive Statistics (NES). Through Markov Chain Monte Carlo (MCMC) sampling, we systematically estimate key parameters, including the non-extensive factor $q$, temperature $T$, and chemical potential $μ$. Our analysis confirms previous findings highlighting the suitability and robustness of Bayesian methods in describing heavy-ion collision data. A subsequent Bayes factor analysis does not provide definitive evidence favoring an Excluded Volume Hadron Resonance Gas (EV-HRG) model over the simpler NES approach. Overall, these results suggest that combining NES with Bayesian inference can effectively model particle distributions and improve parameter estimation accuracy, demonstrating the potential of this approach for future studies on relativistic nuclear interactions.

Bayesian Analysis of Non-extensive Parameters in Au-Au Collisions

TL;DR

This work addresses hadronization in relativistic heavy-ion collisions by applying a Bayesian NES framework to estimate , , and from particle-yield ratios and by comparing NES to an EV-HRG model using Bayes factors. It formalizes a three-parameter inferential setup with uniform priors, uses an affine-invariant MCMC ensemble to sample the posterior, and examines computational choices via diagnostic plots. The study finds robust parameter estimates (e.g., , MeV, MeV) and shows that the Bayes factor does not decisively favor NES over EV-HRG, highlighting the value and limitations of Bayesian model comparison in this context. Overall, the combination of NES with Bayesian inference provides a reproducible and uncertainty-aware framework for modeling particle distributions in Au-Au collisions and suggests avenues for future refinements in relativistic nuclear interaction studies.

Abstract

In this work, a Bayesian statistical framework is employed to analyze particle yield ratios in Au-Au collisions, utilizing Non-Extensive Statistics (NES). Through Markov Chain Monte Carlo (MCMC) sampling, we systematically estimate key parameters, including the non-extensive factor , temperature , and chemical potential . Our analysis confirms previous findings highlighting the suitability and robustness of Bayesian methods in describing heavy-ion collision data. A subsequent Bayes factor analysis does not provide definitive evidence favoring an Excluded Volume Hadron Resonance Gas (EV-HRG) model over the simpler NES approach. Overall, these results suggest that combining NES with Bayesian inference can effectively model particle distributions and improve parameter estimation accuracy, demonstrating the potential of this approach for future studies on relativistic nuclear interactions.

Paper Structure

This paper contains 8 sections, 23 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Bayesian Analysis Framework
  3. Non-extensive statistics
  4. The Excluded Volume Model versus NES model
  5. Model selection
  6. Radius-Parameterized EV-HRG with q-Statistics
  7. Bayes Factor and Model Comparison
  8. Au-Au collision

Figures (1)

  • Figure 1: Posterior distributions for the five free parameters of the EV-HRG model with Tsallis statistics, obtained via MCMC sampling using the emcee sampler. The parameters include the non-extensivity index $q$, temperature $T$, chemical potential $\mu_B$, and the hard-core radii of baryons $R_B$ and mesons $R_M$. The contours represent the 1$\sigma$ and 2$\sigma$ credible regions, while the histograms along the diagonal show the marginalized distributions with median values and corresponding 68% credible intervals.