Statistical aspects of nuclear mass models

Abstract

We study the information content of nuclear masses from the perspective of global models of nuclear binding energies. To this end, we employ a number of statistical methods and diagnostic tools, including Bayesian calibration, Bayesian model averaging, chi-square correlation analysis, principal component analysis and empirical coverage probability. Using a Bayesian framework, we investigate the structure of the four-parameter liquid drop model by considering discrepant mass domains for calibration. We then use the chi-square correlation framework to analyze the 14-parameter Skyrme energy density functional calibrated using homogeneous and heterogeneous datasets. We show that quite a dramatic parameter reduction can be achieved in both cases. The advantage of Bayesian model averaging for improving uncertainty quantification is demonstrated. The statistical approaches used are pedagogically described; in this context this work can serve as a guide for future applications.

A Fast and Calibrated Computer Model Emulator: An Empirical Bayes Approach

“…The semi-empirical mass formula is particularly suitable example, because it provides a good fit for heavy nuclei and somewhat poor fit for light nuclei. This clearly points to the existence of a systematic model discrepancy that is also supported in the literature [37,51,18].…”

“…It is clear from our previous discussions (see (16) in particular) that the model runs play the role of fixed constants in the prior distribution over ζ. The dependence on z in (19) arises by setting Π(ζ|θ, φ) := p(ζ|z, θ, φ), which is the GP prior distribution with the mean function (17) and the covariance function (18).…”

“…The prior distributions for the calibration parameters θ are chose to be wide enough to cover the space of all their reasonable values: The prior distributions for the hyperparameters φ were selected as Gamma(α, β) with the shape parameter α and scale parameter β. They are chosen to be weakly informative so that they correspond to the scale of these parameters given by the literature on nuclear mass models [48,6,29,11,21,27,22,24,23,4,18]. In particular, σ ∼ Gamma(2, 1), η δ ∼ Gamma(10, 1), l Z ∼ Gamma(10, 1), l N ∼ Gamma(10, 1), ν Z ∼ Gamma(10, 1), ν N ∼ Gamma(10, 1), ν i ∼ Gamma(10, 1), i = 1, 2, 3, 4.…”

Variational Inference with Vine Copulas: An efficient Approach for Bayesian Computer Model Calibration

“…The LDM also generally performs better on heavy nuclei as compared to the light nuclei which alludes to the existence of a significant systematic discrepancy between the model and the experimental binding energies (Reinhard et al, 2006;Kejzlar et al, 2020). Namely, we consider the following statistical model…”

“…First, we consider the independent Gaussian distributions centered at the LS estimates θL 2 (in Table 3) with standard deviations 7.5 × SE( θL 2 ) so that the calibration parameters used for generating the model runs are covered roughly within two standard deviations of the priors. Namely, The prior distributions for hyperparameters of the GP 's were selected as Gamma(α, β) with the scale parameter α and rate parameter β, so that they represent a vague knowledge about the scale of these parameters given by the literature on nuclear mass models (Weizsäcker, 1935;Bethe and Bacher, 1936;Myers and Swiatecki, 1966;Fayans, 1998;Kirson, 2008;McDonnell et al, 2015;Kortelainen et al, 2010Kortelainen et al, , 2012Kortelainen et al, , 2014Benzaid et al, 2020;Kejzlar et al, 2020).…”