Constrained functional priors for Bayesian inference of hot QCD matter

Abstract

Bayesian analyses of heavy-ion collisions rely on functional inputs, such as temperature-dependent transport coefficients and the equation of state, whose prior specification remains a significant source of uncertainty. Standard approaches employ low-dimensional parametrizations that can impose artificial correlations and leave the resulting inference sensitive to the assumed functional form. We develop a nonparametric framework for constructing priors over such functions using Gaussian processes, tailored to emulator-based inference in heavy-ion phenomenology. Truncated Karhunen--Lo\`eve expansions yield optimized finite-dimensional representations suitable for use as emulator inputs. We investigate how physical constraints can be incorporated into these priors, demonstrating that rejection-based methods produce non-Gaussian measures and induce nontrivial correlations in the expansion coefficients. By contrast, pushforward constructions enforce the constraints while preserving a tractable Gaussian measure in a latent space. These results provide a systematic framework for incorporating physical constraints into functional priors and clarify their effects on the statistical structure of the finite-dimensional representations used in Bayesian inference.