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Improved information criteria for Bayesian model averaging in lattice field theory
Methodology · Submitted 31 Aug 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that the PPIC has the most appealing theoretical properties and can give the best performance in terms of model-averaging uncertainty, particularly in the presence of noisy data, while the BAIC is a simple and reliable alternative.
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The abstract, sentence by sentence
Bayesian model averaging is a practical method for dealing with uncertainty due to model specification. Use of this technique requires the estimation of model probability weights. In this work, we revisit the derivation of estimators for these model weights. Use of the Kullback-Leibler divergence as a starting point leads naturally to a number of alternative information criteria suitable for Bayesian model weight estimation. We explore three such criteria, known to the statistics literature before, in detail: a Bayesian analogue of the Akaike information criterion which we call the BAIC, the Bayesian predictive information criterion (BPIC), and the posterior predictive information criterion (PPIC). We compare the use of these information criteria in numerical analysis problems common in lattice field theory calculations. We find that the PPIC has the most appealing theoretical properties and can give the best performance in terms of model-averaging uncertainty, particularly in the presence of noisy data, while the BAIC is a simple and reliable alternative.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Bayesian model averaging is a practical method for dealing with uncertainty due to model specification. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | Use of this technique requires the estimation of model probability weights. | background 1.00 | 0.04 | 0.01 | asserted 1.00 |
| s2 | In this work, we revisit the derivation of estimators for these model weights. | contribution 0.95 | 0.81 | 0.02 | asserted 0.90 |
| s3 | Use of the Kullback-Leibler divergence as a starting point leads naturally to a number of alternative information criteria suitable for Bayesian model weight estimation. | method 0.67 | 0.31 | 0.05 | asserted 0.95 |
| s4 | We explore three such criteria, known to the statistics literature before, in detail: a Bayesian analogue of the Akaike information criterion which we call the BAIC, the Bayesian predictive information criterion (BPIC), and the posterior predictive information criterion (PPIC). | contribution 0.56 | 0.45 | 0.04 | asserted 0.99 |
| s5 | We compare the use of these information criteria in numerical analysis problems common in lattice field theory calculations. | method 0.72 | 0.88 | 0.03 | asserted 0.88 |
| s6 | We find that the PPIC has the most appealing theoretical properties and can give the best performance in terms of model-averaging uncertainty, particularly in the presence of noisy data, while the BAIC is a simple and reliable alternative. | result 0.98 | 0.95 | 0.93 | asserted 0.97 |
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The paper
Original abstract
Bayesian model averaging is a practical method for dealing with uncertainty due to model specification. Use of this technique requires the estimation of model probability weights. In this work, we revisit the derivation of estimators for these model weights. Use of the Kullback-Leibler divergence as a starting point leads naturally to a number of alternative information criteria suitable for Bayesian model weight estimation. We explore three such criteria, known to the statistics literature before, in detail: a Bayesian analogue of the Akaike information criterion which we call the BAIC, the Bayesian predictive information criterion (BPIC), and the posterior predictive information criterion (PPIC). We compare the use of these information criteria in numerical analysis problems common in lattice field theory calculations. We find that the PPIC has the most appealing theoretical properties and can give the best performance in terms of model-averaging uncertainty, particularly in the presence of noisy data, while the BAIC is a simple and reliable alternative.
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References
How the literature uses it
35 arXiv papers cite this in 65 sentences
Papers citing it · 17 sentences without a confident label
Uses its method or tool 29 papers
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As described in <ref>, we incorporate the systematic uncertainties due to these variations using Bayesian model averaging (BMA) [ref] .
Light-quark connected intermediate-window contributions to the muon $g-2$ hadronic vacuum polarization from lattice QCD · Data analysis · 1.00
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Continuum extrapolation BMA — Systematic uncertainties are estimated using BMA [ref] , following the procedure and formulae detailed in Refs. [ref] .
Hadronic vacuum polarization for the muon $g-2$ from lattice QCD: Long-distance and full light-quark connected contribution · Introduction · 1.00
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Thus, we determine our final result as well as the statistical and systematic error estimates from an average over the different fit models and kinematic cuts, using weights derived from the Akaike Information Criterion (AIC) [ref] .
Zemach and Friar radii of the proton and neutron from lattice QCD · Model average and final result · 1.00
Cites it as background 6 papers
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We define a model space ${ M_μ}$, which may or may not contain the “true model” $M_$ from which the data arise.[For simplicity of the current discussion, we assume only a single true model; more complicated scenarios are discussed in [ref] .] The true model defines a probability distribution $_M_(z) ≡(z | M_) = (z)$ from which the future data $z$ (in general, a vector of length $d$) are drawn.
Model averaging approaches to data subset selection · Review of model variation formalism · 0.82
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The formulas for the mean and variance from the BMA are given by [equation] where $N_M$ is the number of models and the probability of a specific model $M$ given the data $D$ is defined through the Bayesian Akaike information criterion (BAIC) weight [ref] , [equation] Here, $χ_data^2$ is the standard chi-squared function, not including the contribution of the priors, and $𝐚^⋆$ is the posterior mode (i.e., the best-fit point for the vector of fit parameters $𝐚$ when optimized against the augmented chi-squared function [ref] ). $N_cut$ is the number of data points cut from a data set—in this case, the number of ensembles omitted from a given extrapolation.
Hadronic vacuum polarization for the muon $g-2$ from lattice QCD: Complete short and intermediate windows · Bayesian Model Averaging · 0.97
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While this analysis was nearing completion, an alternate approach to dealing with these challenges was proposed [ref] .
Light Scalar Meson and Decay Constant in SU(3) Gauge Theory with Eight Dynamical Flavors · General Setup · 0.89
What it cites · 34 sentences without a confident label
Builds on 1 paper
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Our current work inherits directly from [ref] , which rigorously studied model averaging for lattice field theory in a Bayesian context.
Bayesian model averaging for analysis of lattice field theory results · Introduction · 0.82
Uses the method or tool of 2 papers
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All Bayesian least squares fits we preformed using the package in Python [ref] , which uses the Gaussian random variable data type from [ref] .
Constrained Curve Fitting · Numerical tests · 1.00
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As a final remark on this example, we note that accuracy of the numerical approximations developed in <ref> have been corroborated in several test cases using the VEGAS algorithm, an importance-sampling-based Monte Carlo integration scheme [ref] .
Adaptive Multidimensional Integration: VEGAS Enhanced · Example 2: Exponential model and subset selection · 0.87
Uses data or values from 1 paper
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The data consists of measurements on 615 configurations from the JLab/W&M/MIT/LANL ensemble (see [ref] for details).
Nucleon Momentum Fraction, Helicity and Transversity from 2+1-flavor Lattice QCD · Example 3: Lattice QCD correlation functions · 0.98
Compares with 2 papers
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We call our revised formula the “Bayesian AIC”, or BAIC, see <ref>; the differences between AIC, $_$ (our name for the formula defined in [ref] ) and BAIC are subtle and irrelevant in the limit that the priors do not influence the results.
Bayesian model averaging for analysis of lattice field theory results · Summary of key results · 0.91
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This result is in agreement with a special case of a more general integral computed in [ref] .
Higher Asymptotics of Laplace's Approximation · Laplace's method · 0.82
Cites as background 18 papers
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For a detailed discussion of Bayesian model averaging with derivations of the basic formulas appearing here, see [ref] .
Bayesian model averaging for analysis of lattice field theory results · Bayesian model averaging procedure · 0.89
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Other explorations of model averaging in a lattice field theory or effective field theory context include [ref] ; the AIC was first used in the context of lattice field theory analysis in [ref] .
Bayesian Methods for Parameter Estimation in Effective Field Theories · Introduction · 0.90
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Other explorations of model averaging in a lattice field theory or effective field theory context include [ref] ; the AIC was first used in the context of lattice field theory analysis in [ref] .
Lattice QCD at the physical point meets SU(2) chiral perturbation theory · Introduction · 0.90
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