Bayesian curve fitting for lattice gauge theorists

TL;DR

This paper introduces a Bayesian method for extracting low-energy spectra from Monte Carlo correlation functions in lattice gauge theory, improving error estimates by incorporating both statistical and systematic uncertainties.

Contribution

It presents a novel Bayesian approach that leverages information from small temporal separations and accounts for various uncertainties in spectral analysis.

Findings

Accurate extraction of low-lying energies from Monte Carlo data.

Inclusion of systematic errors in Bayesian spectral fitting.

Enhanced error estimation method for lattice gauge computations.

Abstract

A new method of extracting the low-lying energy spectrum from Monte Carlo estimates of Euclidean-space correlation functions which incorporates Bayesian inference is described and tested. The procedure fully exploits the information present in the correlation functions at small temporal separations and uses this information in a way consistent with fundamental probabilistic hypotheses. The computed errors on the best-fit energies include both statistical uncertainties and systematic errors associated with the treatment of contamination from higher-lying stationary states. Difficulties in performing the integrals needed to compute these error estimates are briefly discussed.