Bayesian parameter estimation for effective field theories

TL;DR

This paper introduces Bayesian methods for estimating effective field theory parameters, using priors to incorporate theoretical expectations, reduce overfitting, and quantify uncertainties, demonstrated through model problems including lattice data analysis.

Contribution

It develops Bayesian procedures with diagnostic tools for EFT parameter estimation, ensuring unbiased and consistent extraction of low-energy constants from data.

Findings

Bayesian priors improve EFT parameter estimation accuracy.

Diagnostic tools help verify the absence of bias from priors.

Method successfully applied to nucleon mass expansion data.

Abstract

We present procedures based on Bayesian statistics for estimating, from data, the parameters of effective field theories (EFTs). The extraction of low-energy constants (LECs) is guided by theoretical expectations in a quantifiable way through the specification of Bayesian priors. A prior for natural-sized LECs reduces the possibility of overfitting, and leads to a consistent accounting of different sources of uncertainty. A set of diagnostic tools are developed that analyze the fit and ensure that the priors do not bias the EFT parameter estimation. The procedures are illustrated using representative model problems, including the extraction of LECs for the nucleon mass expansion in SU(2) chiral perturbation theory from synthetic lattice data.