Error Estimates of Theoretical Models: a Guide

Abstract

This guide offers suggestions/insights on uncertainty quantification of nuclear structure models. We discuss a simple approach to statistical error estimates, strategies to assess systematic errors, and show how to uncover inter-dependencies by correlation analysis. The basic concepts are illustrated through simple examples. By providing theoretical error bars on predicted quantities and using statistical methods to study correlations between observables, theory can significantly enhance the feedback between experiment and nuclear modeling.

24 pages, 9 figures, submitted to Journal of Physics G

References in corpus (9)

• Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory
• Corrections to nuclear energies and radii in finite oscillator spaces
• Statistical Error analysis of Nucleon-Nucleon phenomenological potentials
• Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization
• Neutron skins and neutron stars
• Dependence of single-particle energies on coupling constants of the nuclear energy density functional
• Event-by-event study of prompt neutrons from 239Pu(n,f)
• Error analysis of nuclear mass fits
• Neutron matter based on consistently evolved chiral three-nucleon interactions

Cited by in corpus (185)

• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Building relativistic mean field models for finite nuclei and neutron stars
• The Compression-Mode Giant Resonances and Nuclear Incompressibility
• Time-dependent density-functional description of nuclear dynamics
• Nuclear Equation of State from ground and collective excited state properties of nuclei
• Bayesian approach to model-based extrapolation of nuclear observables
• Future of Nuclear Fission Theory
• r-Process Nucleosynthesis: Connecting Rare-Isotope Beam Facilities with the Cosmos
• Bayesian truncation errors in chiral effective field theory: nucleon-nucleon observables
• Uncertainty analysis and order-by-order optimization of chiral nuclear interactions
• Octupole deformation in the ground states of even-even nuclei: a global analysis within the covariant density functional theory
• Information content of the parity-violating asymmetry in ${}^{208}$Pb
• Neutron skins of atomic nuclei: per aspera ad astra
• Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements
• Towards the global description of nuclear charge radii: exploring the Fayans energy density functional
• Symmetry Energy of Nucleonic Matter With Tensor Correlations
• A recipe for EFT uncertainty quantification in nuclear physics
• Bayesian parameter estimation for effective field theories
• Exploring sd-shell nuclei from two- and three-nucleon interactions with realistic saturation properties
• Fission barriers and probabilities of spontaneous fission for elements with Z$\ge$100
• Dipole polarizability of 120Sn and nuclear energy density functionals
• New relativistic effective interaction for finite nuclei, infinite nuclear matter and neutron stars
• Impact of nuclear mass uncertainties on the $r$-process
• Global description of beta-minus decay in even-even nuclei with the axially-deformed Skyrme finite amplitude method
• The neutron drip line: single-particle degrees of freedom and pairing properties as sources of theoretical uncertainties
• Combined theoretical analysis of the parity-violating asymmetry for ${}^{48}$Ca and ${}^{208}Pb$
• Get on the BAND Wagon: A Bayesian Framework for Quantifying Model Uncertainties in Nuclear Dynamics
• Covariant density functional theory: Reexamining the structure of superheavy nuclei
• Exploring Bayesian parameter estimation for chiral effective field theory using nucleon-nucleon phase shifts
• Statistical Error analysis of Nucleon-Nucleon phenomenological potentials
• Bayesian analysis of the crust-core transition with a compressible liquid-drop model
• Opportunities for Fundamental Physics Research with Radioactive Molecules
• Isovector properties of the Gogny interaction
• Properties of nuclei in the nobelium region studied within the covariant, Skyrme, and Gogny energy density functionals
• Quantified Gamow Shell Model interaction for $psd$-shell nuclei
• Higher-order symmetry energy and neutron star core-crust transition with Gogny forces
• Parametric correlations in energy density functionals
• Correlating Schiff moments in the light actinides with octupole moments
• Assessing theoretical uncertainties in fission barriers of superheavy nuclei
• Isospin-symmetry breaking in masses of $N\simeq Z$ nuclei
• Hyperheavy nuclei: existence and stability
• Linear response of homogeneous nuclear matter with energy density functionals
• Central depression in nucleonic densities: Trend analysis in nuclear density-functional-theory approach
• Extension of nuclear landscape to hyperheavy nuclei
• Beyond the charge radius: the information content of the fourth radial moment
• Error Analysis in Nuclear Density Functional Theory
• Octupole deformation in the ground states of even-even $Z\sim 96,N\sim 196$ actinides and superheavy nuclei
• Nuclear charge and neutron radii and nuclear matter: trend analysis
• Infrared extrapolations for atomic nuclei
• Statistical aspects of nuclear mass models
• Implications of parity-violating electron scattering experiments on ${}^{48}$Ca (CREX) and ${}^{208}$Pb (PREX-II) for nuclear energy density functionals
• The propagation of statistical errors in covariant density functional theory: ground state observables and single-particle properties
• Precise Determination of Charge Dependent Pion-Nucleon-Nucleon Coupling Constants
• Charge radii of ${}^{55,56}$Ni reveal a surprisingly similar behavior at $N=28$ in Ca and Ni isotopes
• Bootstrapping the statistical uncertainties of NN scattering data
• Towards Precise and Accurate Calculations of Neutrinoless Double-Beta Decay: Project Scoping Workshop Report
• Information content of the differences in the charge radii of mirror nuclei
• Covariance analysis for Energy Density Functionals and instabilities
• Spectroscopic properties of nuclear Skyrme energy density functionals
• Constraining the surface properties of effective Skyrme interactions
• Sensitivity of elements of the symmetry energy of nuclear matter to the properties of neutron-rich systems
• Tides in merging neutron stars: Consistency of the GW170817 event with experimental data on finite nuclei
• Solution of Hartree-Fock-Bogoliubov equations and fitting procedure using N2LO Skyrme pseudo-potential in spherical symmetry
• Numerical accuracy of mean-field calculations in coordinate space
• Ab Initio Derivation of Model Energy Density Functionals
• Nuclear dipole polarizability from mean-field modeling constrained by chiral effective field theory
• Constraining the symmetry energy content of nuclear matter from nuclear masses: a covariance analysis
• Statistical uncertainties of a chiral interaction at next-to-next-to leading order
• Low-energy nuclear physics and global neutron star properties
• Error estimates for the Skyrme-Hartree-Fock model
• Covariant density functional theory input for r-process simulations in actinides and superheavy nuclei: the ground state and fission properties
• Solution of universal nonrelativistic nuclear DFT equations in the Cartesian deformed harmonic-oscillator basis. (IX) HFODD (v3.06h): a new version of the program
• The impact of the surface energy coefficient on the deformation properties of atomic nuclei as predicted by Skyrme energy density functionals
• Microscopically constrained mean field models from chiral nuclear thermodynamics
• Global calculations on the microscopic energies and nuclear deformations: Isospin dependence of the spin-orbit coupling
• Functional Renormalization Group and Kohn-Sham scheme in Density Functional Theory
• Sensitivity of the fusion cross section to the density dependence of the symmetry energy
• Parametrisations of relativistic energy density functionals with tensor couplings
• Evolution of the dipole polarizability in the stable tin isotope chain
• Challenges in Nuclear Structure Theory
• Estimating parameter uncertainty in binding-energy models by the frequency-domain bootstrap
• Derivative-free optimization for parameter estimation in computational nuclear physics
• Impact of statistical uncertainties on the composition of the outer crust of a neutron star
• Nonlocal energy density functionals for pairing and beyond-mean-field calculations
• Uncertainty decomposition method and its application in the liquid drop model
• Uncertainty Quantification and Propagation in Nuclear Density Functional Theory
• Sloppy nuclear energy density functionals: effective model reduction
• New effective interactions for hypernuclei in density dependent relativistic mean field model
• EoS constraints from nuclear masses and radii in a meta-modeling approach
• Exploring experimental conditions to reduce uncertainties in the optical potential
• Effect of isovector scalar meson on equation of state of dense matter within relativistic mean field model
• Isospin coupling-channel decomposition of nuclear symmetry energy in covariant density functional theory
• Electromagnetic Properties of Indium Isotopes Elucidate the Doubly Magic Character of ${}^{100}$Sn
• $\alpha$ Decay Half-life Estimation and Uncertainty Analysis
• Confirmation of $g_{\mathrm{A}}$ quenching using the revised spectrum-shape method for the analysis of the ${}^{113}$Cd $\beta$-decay as measured with the COBRA demonstrator
• Unveiling the correlations of tidal deformability with the nuclear symmetry energy parameters
• Gamow Shell Model description of Li isotopes and their mirror partners
• Isobaric Multiplet Mass Equation within nuclear Density Functional Theory
• Modeling Charmonium-$\eta$ Decays of $J^{PC}=1^{--}$ Higher Charmonia
• CREX- and PREX-II-motivated relativistic interactions and their implications for the bulk properties of nuclear matter and neutron stars
• A methodology for theory uncertainties in the SMEFT
• Extended Skyrme pseudo-potential deduced from infinite matter properties
• Error analysis of nuclear forces and effective interactions
• Information and statistics: a new paradigm in theoretical nuclear physics
• Symmetry energy effect on the secondary component of GW190814 as a neutron star
• Applications of Neural Networks in Hadron Physics
• Relativistic Mean Field Model parameterizations in the light of GW170817, GW190814, and PSR J0740 + 6620
• Pasta properties of the neutron star within effective relativistic mean-field model
• Low-energy M1 excitations in ${}^{208}$Pb and the spin channel of the Skyrme energy-density functional
• Properties of the neutron star crust: Quantifying and correlating uncertainties with improved nuclear physics
• An introduction to Bootstrap for nuclear physics
• Crustal properties of a neutron star within an effective relativistic mean-field model
• Effective theory for the non-rigid rotor in an electromagnetic field: Toward accurate and precise calculations of E2 transitions in deformed nuclei
• Extrapolating from neural network models: a cautionary tale
• Triton binding energy with realistic precision
• Uncertainty quantification of an empirical shell-model interaction using principal component analysis
• Light Nuclei from Lattice QCD: Spectrum, Structure and Reactions
• Uncertainty quantification in nuclear shell model
• Meson-baryon scattering to one-loop order in heavy baryon chiral perturbation theory
• Light pseudoscalar meson and heavy meson scattering lengths to $\mathcal{O}(p^4)$ in heavy meson chiral perturbation theory
• Gamow-Teller and double-beta decays of heavy nuclei within an effective theory
• Observational constraint from the heaviest pulsar PSR J0952-0607 on the equation of state of dense matter in relativistic mean field model
• Low-energy bound states, resonances, and scattering of light ions
• Relativistic approach for the determination of nuclear and neutron star properties in consideration of PREX-II results
• Optimizing relativistic energy density functionals: covariance analysis
• Model nuclear energy density functionals derived from ab initio calculations
• Estimating the relevance of predictions from nuclear mean-field models
• Constraining nuclear matter parameters from correlation systematics:a mean-field perspective
• Non-parametric Bayesian approach to extrapolation problems in configuration interaction methods
• Statistical error propagation in ab initio no-core full configuration calculations of light nuclei
• The nucleon effective mass and its isovector splitting
• Reappraisal of the limit on the variation in $\alpha$ implied by Oklo
• Pion-nucleon scattering to $\mathcal{O}(p^3)$ in heavy baryon SU(3) chiral perturbation theory
• Odd-even staggering in neutron drip line nuclei
• Theoretical uncertainties of the elastic nucleon-deuteron scattering observables
• Bayesian inference on the isospin splitting of nucleon effective mass from giant resonances in ${}^{208}$Pb
• Optimization and Supervised Machine Learning Methods for Fitting Numerical Physics Models without Derivatives
• Propagation of uncertainties in the nuclear DFT models
• Addressing spectroscopic quality of covariant density functional theory
• Principal component analysis within nuclear structure
• The phonon-coupling model for Skyrme forces
• Uncertainty propagation within the UNEDF models
• Two-neutrino double-beta decay matrix elements based on relativistic nuclear energy density functional
• Kaon-nucleon scattering to one-loop order in heavy baryon chiral perturbation theory
• Calibration of Energy Density Functionals with Deformed Nuclei
• Properties of spherical and deformed nuclei using regularized pseudopotentials in nuclear DFT
• Anchor-based optimization of energy density functionals
• Statistical learnability of nuclear masses
• Moving Beyond Chi-Squared in Nuclei and Neutron Stars
• Pion-nucleon scattering to order $p^4$ in SU(3) heavy baryon chiral perturbation theory
• Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms II: Charge Exchange
• Effects of Many-body Interactions in Hypernuclei with Korea-IBS-Daegu-SKKU Functionals
• Quantifying statistical uncertainties in ab initio nuclear physics using Lagrange multipliers
• Bayesian averaging of computer models with domain discrepancies: a nuclear physics perspective
• Nuclear charge radii of germanium isotopes around $N$ = 40
• Relativistic Hartree-Fock Chiral Lagrangians with confinement, nucleon finite size and short-range effects
• Phase shifts of the light pseudoscalar meson and heavy meson scattering in heavy meson chiral perturbation theory
• The nucleardatapy toolkit for simple access to experimental nuclear data, astrophysical observations, and theoretical predictions
• Landau parameters for energy density functionals generated by local finite-range pseudopotentials
• Sensitivity of predictions in an effective model -- application to the chiral critical end point position in the Nambu--Jona-Lasinio model
• Constructing a simulation surrogate with partially observed output
• Covariance analysis of finite temperature density functional theory: symmetric nuclear matter
• Shape polarization in the tin isotopes near $N=60$ from precision $g$-factor measurements on short-lived $11/2^{-}$ isomers
• Impact of $\Xi$-Hypernuclear Constraints on Relativistic Equation of State and Properties of Hyperon Stars
• Impact of choices for center-of-mass correction energy on the surface energy of Skyrme energy density functionals
• Subspace-projected multireference covariant density functional theory
• Pion-nucleon scattering with decuplet contribution in heavy baryon SU(3) chiral perturbation theory
• Effective field theories for collective excitations of atomic nuclei
• Stability of the manifold boundary approximation method for reductions of nuclear structure models
• Ab initio models of atomic nuclei: challenges and new ideas
• Binding energies and pairing gaps in semi-magic nuclei obtained using new regularized higher-order EDF generators
• Classical and Bayesian error analysis of the relativistic mean-field model for doubly magic nuclei
• Exploring the possible two-proton radioactivity of ${}^{38,39}$Ti
• Analytic insights on the information content of new observables
• Structure of Krypton Isotopes using the Generalised Bohr Hamiltonian Method
• Quantification of Uncertainties in Nuclear Density Functional theory
• Pulsed, Polarized X-ray Emission from Neutron Star Surfaces: the Effects of Vacuum Birefringence in the Magnetosphere
• Universal trend of charge radii of even-even Ca-Zn nuclei
• Conformal prediction for uncertainties in nucleon-nucleon scattering
• Meson-baryon scattering lengths without annihilation diagrams to order $p^4$ in heavy baryon chiral perturbation theory
• Impact of error analysis on the composition the outer crust of a neutron star
• Uncertainty evaluation and correlation analysis of single-particle energies in phenomenological nuclear mean field: An investigation of propagating uncertainties for independent model parameters
• The Falsification of Nuclear Forces
• The nuclear matter density functional under the nucleonic hypothesis
• Statistical correlations of nuclear quadrupole deformations and charge radii