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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.

Model averaging is a useful and robust method for dealing with model uncertainty in statistical analysis. Often, it is useful to consider data subset selection at the same time, in which model selection criteria are used to compare models across different subsets of the data. Two different criteria have been proposed in the literature for how the data subsets should be weighted. We compare the two criteria closely in a unified treatment based on the Kullback-Leibler divergence, and conclude that one of them is subtly flawed and will tend to yield larger uncertainties due to loss of information. Analytical and numerical examples are provided.

We present results for the dominant light-quark connected contribution to the long-distance window (LD) of the hadronic vacuum polarization contribution (HVP) to the muon \\(g-2\\) from lattice quantum chromodynamics (QCD). Specifically, with a new determination of the lattice scale on MILC's physical-mass HISQ ensembles, using the \\(^-\\) baryon mass, we obtain a result of \\(400.2(2.3)_stat(3.7)_syst[4.3]_total 10^-10\\). Summing this result with our recent determinations of the light-quark connected contributions to the short- (SD) and intermediate-distance (W) windows, we obtain a sub-percent precision determination of the light-quark-connected contribution to HVP of \\(655.5(2.3)_stat(3.9)_syst[4.5]_total 10^-10\\). Finally, as a consistency check, we verify that an independent analysis of the full contribution is in agreement with the sum of individual windows. We discuss our future plans for improvements of our HVP calculations to meet the target precision of the Fermilab \\(g-2\\) experiment.

We present complete results for the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment \\(a_\\) in the short- and intermediate-distance window regions, which account for roughly 10% and 35% of the total HVP contribution to \\(a_\\), respectively. In particular, we perform lattice-QCD calculations for the isospin-symmetric connected and disconnected contributions, as well as corrections due to strong isospin-breaking. For the short-distance window observables, we investigate the so-called log-enhancement effects as well as the significant oscillations associated with staggered quarks in this region. For the dominant, isospin-symmetric light-quark connected contribution, we obtain \\(a^ll,\\,SD_(conn.) = 48.139(11)_stat(91)_syst[92]_total 10^-10\\) and \\(a^ll,\\,W_(conn.) = 206.90(14)_stat(61)_syst[63]_total 10^-10\\). We use Bayesian model averaging to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are \\(a^SD_ = 69.05(1)_stat(21)_syst[21]_total 10^-10\\) and \\(a^W_ = 236.45(17)_stat(83)_syst[85]_total 10^-10\\). This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few permille level.

The gradient-flow scale \\(w_0\\) in lattice QCD is determined using the mass of the \\(\\Omega^-\\) baryon to set the physical scale. Nine ensembles using the highly improved staggered quark (HISQ) action with lattice spacings of 0.15 fm down to 0.04 fm are used, seven of which have nearly physical light-quark masses. Electromagnetic corrections to the \\(\\Omega^-\\) mass are defined in order to compute a pure-QCD \\(\\Omega\\) mass. The final result is \\(w_0 = 0.17187(68)\\) fm, corresponding to a relative uncertainty of 0.40% and a central value in good agreement with previous calculations in the literature.

We present results for the dominant light-quark connected contribution to the long-distance window (LD) of the hadronic vacuum polarization contribution (HVP) to the muon \\(g-2\\) from lattice quantum chromodynamics (QCD). Specifically, with a new determination of the lattice scale on MILC's physical-mass HISQ ensembles, using the \\(\\Omega^-\\) baryon mass, we obtain a result of \\(a^{ll,\\,{\\mathrm{LD}}}_{\\mu}(\\mathrm{conn.}) = 401.2(2.3)_{\\mathrm{stat}}(3.6)_{\\mathrm{syst}}[4.3]_{\\mathrm{total}} \\times 10^{-10}\\). In addition, following up on our recent work on the short- (SD) and intermediate-distance (W) windows, we report updated values for these quantities with this new scale-setting determination. Summing these individual window contributions enables a sub-percent precision determination of the light-quark-connected contribution to HVP of \\(a^{ll}_{\\mu}(\\mathrm{conn.}) = 656.2(1.9)_{\\mathrm{stat}}(4.0)_{\\mathrm{syst}}[4.4]_{\\mathrm{total}} \\times 10^{-10}\\). Finally, as a consistency check, we verify that an independent analysis of the full contribution is in agreement with the sum of individual windows. We discuss our future plans for improvements of our HVP calculations to meet the target precision of the Fermilab \\(g-2\\) experiment.

We present complete results for the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment \\(a_\\mu\\) in the short- and intermediate-distance window regions, which account for roughly 10% and 35% of the total HVP contribution to \\(a_\\mu\\), respectively. In particular, we perform lattice-QCD calculations for the isospin-symmetric connected and disconnected contributions, as well as corrections due to strong isospin-breaking. For the short-distance window observables, we investigate the so-called log-enhancement effects as well as the significant oscillations associated with staggered quarks in this region. For the dominant, isospin-symmetric light-quark connected contribution, we obtain \\(a^{ll,\\,{\\mathrm{SD}}}_{\\mu}(\\mathrm{conn.}) = 48.116(16)(94)[96] \\times 10^{-10}\\) and \\(a^{ll,\\,{\\mathrm{W}}}_{\\mu}(\\mathrm{conn.}) = 207.06(17)(63)[66] \\times 10^{-10}\\). We use Bayesian model averaging combined with a global bootstrap to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are \\(a^{{\\mathrm{SD}}}_{\\mu} = 69.01(2)(21)[21] \\times 10^{-10}\\) and \\(a^{{\\mathrm{W}}}_{\\mu} = 236.57(20)(94)[96] \\times 10^{-10}\\). This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few permille level.