Bayesian model averaging for analysis of lattice field theory results

TL;DR

This paper introduces a Bayesian model averaging approach to analyze lattice field theory data, effectively incorporating model uncertainty and automating data subset selection for more reliable physical results.

Contribution

It develops a Bayesian framework for model averaging in lattice data analysis, including formulas and approximations for least-squares fitting and data subset selection.

Findings

Model averaging captures systematic errors from model choice.

Automates the selection of fit ranges in lattice data analysis.

Demonstrates effectiveness with mock and real data.

Abstract

Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be considered for the same lattice data. Model averaging, which amounts to a probability-weighted average over all model variations, can incorporate systematic errors associated with model choice without being overly conservative. We discuss the framework of model averaging from the perspective of Bayesian statistics, and give useful formulae and approximations for the particular case of least-squares fitting, commonly used in modeling lattice results. In addition, we frame the common problem of data subset selection (e.g. choice of minimum and maximum time separation for fitting a two-point correlation function) as a model selection problem and study model averaging as a straightforward alternative to manual selection of fit ranges. Numerical examples involving both mock and real lattice data are given.