一种新的贝叶斯谱函数重构方法
A new Bayesian approach to the reconstruction of spectral functions
摘要：
我们提出了一种新的方法，从欧几里德相关数据，使现代贝叶斯概念的光谱重建。它是基于一个公理合理的无量纲先验分布，在恒定的先验函数$m(ω)$的情况下，只印平滑重建的频谱。此外，我们能够分析地整合出先验中唯一相关的整体超参数$α$，从而消除了例如在最大熵方法中发现的高斯近似的必要性。利用拟牛顿极小化器和高精度算法，我们能够在全$N_ω\gg N_τ$维搜索空间中找到$P[ρ|D]$的唯一全局极值。该方法实际上产生逐步改善重建结果，如果所提供的输入数据的质量增加，而不引入人工峰结构，经常遇到的MEM。为了支持这些声明，我们提出模拟数据分析的情况下，零宽度δ峰和更现实的情况下，微扰欧几里德威尔逊圈以及威尔逊线相关库仑规。
英文摘要：
We present a novel approach for the reconstruction of spectra from Euclidean correlator data that makes close contact to modern Bayesian concepts. It is based upon an axiomatically justified dimensionless prior distribution, which in the case of constant prior function $m(ω)$ only imprints smoothness on the reconstructed spectrum. In addition we are able to analytically integrate out the only relevant overall hyper-parameter $α$ in the prior, removing the necessity for Gaussian approximations found e.g. in the Maximum Entropy Method. Using a quasi-Newton minimizer and high-precision arithmetic, we are then able to find the unique global extremum of $P[ρ|D]$ in the full $N_ω\gg N_τ$ dimensional search space. The method actually yields gradually improving reconstruction results if the quality of the supplied input data increases, without introducing artificial peak structures, often encountered in the MEM. To support these statements we present mock data analyses for the case of zero width delta peaks and more realistic scenarios, based on the perturbative Euclidean Wilson Loop as well as the Wilson Line correlator in Coulomb gauge.
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