Computational budget optimization for Bayesian parameter estimation in heavy ion collisions

TL;DR

This paper investigates how to optimally allocate computational resources between sampling parameters and simulating collisions in Bayesian inference for heavy ion collision models, to improve constraints on nuclear matter properties.

Contribution

It introduces a method to balance emulator and statistical uncertainties by optimizing the number of parameter samples and collision simulations within a fixed computational budget.

Findings

Optimal constraints occur when parameter samples are slightly fewer than collision simulations.

Emulator interpolation uncertainties significantly impact Bayesian inference accuracy.

Trade-offs between sampling density and simulation depth are quantified for better resource allocation.

Abstract

Bayesian parameter estimation provides a systematic approach to compare heavy ion collision models with measurements, leading to constraints on the properties of nuclear matter with proper accounting of experimental and theoretical uncertainties. Aside from statistical and systematic model uncertainties, interpolation uncertainties can also play a role in Bayesian inference, if the model's predictions can only be calculated at a limited set of model parameters. This uncertainty originates from using an emulator to interpolate the model's prediction across a continuous space of parameters. In this work, we study the trade-offs between the emulator (interpolation) and statistical uncertainties. We perform the analysis using spatial eccentricities from the T$_\mathrm{R}$ENTo model of initial conditions for nuclear collisions. Given a fixed computational budget, we study the optimal compromise between the number of parameter samples and the number of collisions simulated per parameter sample. For the observables and parameters used in the present study, we find that the best constraints are achieved when the number of parameter samples is slightly smaller than the number of collisions simulated per parameter sample.