用于高温QCD物质贝叶斯推理的约束函数先验
Constrained functional priors for Bayesian inference of hot QCD matter
- Universidade de São Paulo（圣保罗大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对重离子碰撞贝叶斯推理中函数先验的不确定性问题，开发基于高斯过程的非参数框架，提出两种约束纳入方法，为物理约束的整合提供系统方案。
AI中文摘要：
重离子碰撞的贝叶斯推理依赖于温度相关输运系数、物态方程等函数输入，其先验设定仍是不确定性的重要来源。标准方法采用低维参数化，会引入人为关联，使推理对假设的函数形式敏感。我们开发了一种基于高斯过程的非参数框架，用于构建此类函数的先验，适配重离子现象学中基于模拟器的推理。截断Karhunen–Loève展开可生成优化的有限维表示，适合作为模拟器输入。我们研究如何将物理约束纳入这些先验，证明基于拒绝的方法会产生非高斯测度，并在展开系数中引入非平凡关联；相比之下，推前构造可在保持潜在空间中易处理高斯测度的同时强制执行约束。这些结果提供了将物理约束纳入函数先验的系统框架，并阐明了它们对贝叶斯推理中所用有限维表示的统计结构的影响。
英文摘要：
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--Loève 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.
