Bayesian analysis of heavy ion collisions with the heavy ion computational framework Trajectum

Abstract

We introduce a model for heavy ion collisions named Trajectum, which includes an expanded initial stage with a variable free streaming velocity v fs and a hydrodynamic stage with three varying second order transport coefficients. We describe how to obtain a Gaussian Emulator for this 20-parameter model and show results for key observables. This emulator can be used to obtain Bayesian posterior estimates on the parameters, which we test by an elaborate closure test as well as a convergence study. Lastly, we employ the optimal values of the parameters found in [1] to perform a detailed comparison to experimental data from PbPb and pPb collisions. This includes both observables that have been used to obtain these values as well as wider transverse momentum ranges and new observables such as correlations of event-plane angles.

Non-Abelian electric field correlator at NLO for dark matter relic abundance and quarkonium transport

“…[121] for a review) may be useful to calculate this correlator. It can also be extracted from experimental data on quarkonium suppression in heavy ion collisions, by using Bayesian analysis [122,123]. Anisotropic effects on the electric field correlator can also be studied in a similar way to refs.…”

Efficient emulation of relativistic heavy ion collisions with transfer learning

“…, x q ) is the uniform probability measure over X −j , the parameter space X omitting the j-th parameter. The first-order Sobol' index (13) thus quantifies the importance of parameter x j , by taking the ratio of Var Xj (E X−j (δ(X)|X j )), the variance accounted for by the main effects E X−j (δ(X)|X j ), over Var X (Y ), the total variance of δ(•) over all parameters. For costly simulations such as for heavy ion collisions, the integral in ( 14) can be expensive to evaluate.…”

“…Bayesian inference or Bayesian parameter estimation is a modern statistical method that provides a way to reliably infer the properties of QGP, by accounting methodically for both theoretical and experimental uncertainties. Tremendous progress has been made in the study of relativistic heavy ion collisions over the past decade by providing increasingly reliable constraints and error estimates for the properties of QGP using Bayesian statistical techniques [3][4][5][6][7][8][9][10][11][12][13][14]. As both the model and data have uncertainties, comparing them results in a probability distribution for the model parameters, specifying the probability for a model with a given set of parameters to provide predictions that agree with the experimental observations.…”

“…Emulators are machine learning models that provide a computationally efficient prediction of the simulator over the parameter space when trained on a sparse set of full simulation data. While a modeler can choose from a wide range of learning models (e.g., linear regression, decision trees, neural networks) as surrogates for expensive simulations, the standard practice in relativistic nuclear physics [4][5][6][7][8][9][10][11][12][13][14] has been to use Gaussian Process (GP) emulators [17]. There are two reasons for this: (i) GPs provide a flexible non-parametric framework for emulation modeling and (ii) they also provide an efficient quantifica-tion of the predictive uncertainty associated with the interpolation between training points in the n-dimensional parameter space.…”

Determining the jet transport coefficient q̂ from inclusive hadron suppression measurements using Bayesian parameter estimation

“…Bayesian inference has been utilized previously to extract parameters of the QGP from heavy-ion collision data, in particular the specific shear viscosity η/s [82][83][84][85] and the equation of state (EoS) [86], with the latter result agreeing well with lattice QCD calculations. See also [87]. This approach has likewise been used to study the heavy quark diffusion coefficient of the QGP [88].…”