A novel Bayesian approach to spectral function reconstruction

TL;DR

This paper introduces a new Bayesian method for reconstructing spectral functions from Euclidean correlator data, improving upon existing techniques by addressing prior assumptions and hyperparameter integration.

Contribution

The authors develop a novel Bayesian approach with new axioms for the prior, eliminating flat directions and explicitly integrating hyperparameters, advancing spectral function inference methods.

Findings

Successfully tested on mock data for heavy quark potential

Established data quality requirements for lattice QCD extraction

Provided improved potential estimates from lattice QCD data

Abstract

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the MEM. We present a realistic test of our method in the context of the non-perturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. An improved potential estimation from previously investigated quenched lattice QCD correlators is provided.