Heavy-ion collisions provide a window into the properties of many-body systems of deconfined quarks and gluons. Understanding the collective properties of quarks and gluons is possible by comparing models of heavy-ion collisions to measurements of the distribution of particles produced at the end of the collisions. These model-to-data comparisons are extremely challenging, however, because of the complexity of the models, the large amount of experimental data, and their uncertainties. Bayesian inference provides a rigorous statistical framework to constrain the properties of nuclear matter by systematically comparing models and measurements.
This review covers model emulation and Bayesian methods as applied to model-to-data comparisons in heavy-ion collisions. Replacing the model outputs (observables) with Gaussian process emulators is key to the Bayesian approach currently used in the field, and both current uses of emulators and related recent developments are reviewed. The general principles of Bayesian inference are then discussed along with other Bayesian methods, followed by a systematic comparison of seven recent Bayesian analyses that studied quark-gluon plasma properties, such as the shear and bulk viscosities. The latter comparison is used to illustrate sources of differences in analyses, and what it can teach us for future studies.
Cost-efficient Bayesian emulation of quark-gluon plasma modeling with variable statistical precision
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of California, Berkeley（加州大学伯克利分校）；Duke University（杜克大学）；JMP Statistical Discovery LLC（JMP统计发现有限责任公司）
High-Dimensional Bayesian Calibration of Expensive Nuclear Models with Differentiable Emulation
School of Physics Science and Engineering, Tongji University（同济大学物理科学与工程学院）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院现代物理研究所南方核科学理论中心）
Joint Bayesian analysis of soft and high-$p_\perp$ probes yields tighter constraints on QGP properties
Faculty of Biology, University of Belgrade（贝尔格莱德大学生物学院）；Institute of Physics Belgrade, University of Belgrade（贝尔格莱德大学物理研究所）；Serbian Academy of Sciences and Arts（塞尔维亚科学与艺术学院）
Bayesian constraints on the transport coefficients $η/s$ and $ζ/s$ from spin polarization in relativisitic heavy-ion collisions
Università di Firenze（佛罗伦萨大学）；Dipartimento di Fisica, Università di Firenze（佛罗伦萨大学物理系）；Variable Energy Cyclotron Centre（变能回旋加速器中心）；INFN Sezione di Firenze（佛罗伦萨意大利国家核物理研究所）
Applying Bayesian parameter estimation to relativistic heavy-ion collisions: simultaneous characterization of the initial state and quark-gluon plasma medium
Bayesian Inference of Heavy-Quark Dissipation and Jet Transport Parameters from D-Meson observables in heavy-ion collisions at the LHC energies
School of Mathematics and Physics, China University of Geosciences（中国地质大学数学与物理学院）；Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University（华中师范大学夸克与轻子物理教育部重点实验室及粒子物理研究所）；Helmholtz Research Academy Hesse for FAIR (HFHF), GSI Helmholtz Center for Heavy Ion Physics（黑森FAIR亥姆霍兹研究学院（GSI重离子物理中心））；Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität（约翰·沃尔夫冈·歌德大学理论物理研究所）
Bayesian inference of event-by-event collision geometry from charged-particle multiplicity in heavy-ion collisions
State Key Laboratory of Heavy Ion Science and Technology, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所重离子物理与技术国家重点实验室）；Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) & Institute of Modern Physics, Fudan University（复旦大学核物理与离子束应用教育部重点实验室、近代物理研究所）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（国家自然科学基金委与复旦大学理论核物理联合研究中心）；Key Laboratory of Quark and Lepton Physics (MOE) & Institute of Particle Physics, Central China Normal University（华中师范大学夸克与轻子物理教育部重点实验室、粒子物理研究所）；University of Heidelberg（海德堡大学）
Disentangling flow and nonflow correlations via Bayesian unfolding of the event-by-event distributions of harmonic coefficients in ultrarelativistic heavy-ion collisions
