Error Estimates of Theoretical Models: a Guide

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-dependences 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.

[1]  Paul-Gerhard Reinhard,et al.  Variations on a theme by Skyrme: A systematic study of adjustments of model parameters , 2009 .

[2]  J. Dobaczewski,et al.  Error analysis of nuclear mass fits , 2008, 0806.1914.

[3]  G. Colò,et al.  Covariance analysis for energy density functionals and instabilities , 2014, 1406.1885.

[4]  W. Nazarewicz,et al.  Information content of the weak-charge form factor , 2013, 1308.1659.

[5]  M. Bertolli.  Correlation testing for nuclear density functional theory , 2012, 1208.1525.

[6]  P.Ring,et al.  Nuclear landscape in covariant density functional theory , 2013, 1309.3289.

[7]  Stefan M. Wild,et al.  Nuclear Energy Density Optimization , 2010, 1005.5145.

[8]  Christina Kluge,et al.  Data Reduction And Error Analysis For The Physical Sciences , 2016 .

[9]  W. Nazarewicz,et al.  Energy density functional for nuclei and neutron stars , 2012, 1211.6292.

[10]  S. Shafer.  All models are wrong. , 2012, Anesthesiology.

[11]  S. Gandolfi,et al.  The maximum mass and radius of neutron stars and the nuclear symmetry energy , 2011, 1101.1921.

[12]  Andrew W. Steiner,et al.  THE NEUTRON STAR MASS–RADIUS RELATION AND THE EQUATION OF STATE OF DENSE MATTER , 2012, 1205.6871.

[13]  M. Kortelainen,et al.  Dependence of single-particle energies on coupling constants of the nuclear energy density functional , 2008, 0803.2291.

[14]  B. Gebremariam,et al.  Microscopically based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization , 2010, 1009.3452.

[15]  R. T. Birge,et al.  The Calculation of Errors by the Method of Least Squares , 1932 .

[16]  George F. Bertsch,et al.  Fitting theories of nuclear binding energies , 2005 .

[17]  R. Vogt,et al.  Event-by-event study of prompt neutrons from 239Pu(n,f) , 2009, 0907.5045.

[18]  E. Ruiz Arriola,et al.  Error Analysis of Nuclear Matrix Elements , 2013, 1310.7456.

[19]  Silvio Funtowicz,et al.  Are all models wrong? , 2020, Computational and systems oncology.

[20]  W. Myers,et al.  Nuclear ground state masses and deformations , 1995 .

[21]  R. J. Furnstahl,et al.  Corrections to Nuclear Energies and Radii in Finite Oscillator Spaces , 2012, 1207.6100.

[22]  M. Kortelainen,et al.  Neutron skin uncertainties of Skyrme energy density functionals , 2013, 1307.4223.

[23]  Symmetry energy in nuclear density functional theory , 2013, 1307.5782.

[24]  E. Brown,et al.  THE EQUATION OF STATE FROM OBSERVED MASSES AND RADII OF NEUTRON STARS , 2010, 1005.0811.

[25]  Saltelli Andrea,et al.  When all models are wrong: More stringent quality criteria are needed for models used at the science-policy interface , 2014 .

[26]  Statistical significance of theoretical predictions: A new dimension in nuclear structure theories (I) , 2011 .

[27]  G.F.Bertsch,et al.  Fitting theories of nuclear binding energies , 2004, nucl-th/0412091.

[28]  A. Schwenk,et al.  Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory. , 2012, Physical review letters.

[29]  George E. P. Box,et al.  Empirical Model‐Building and Response Surfaces , 1988 .

[30]  G. Box.  Science and Statistics , 1976 .

[31]  Stefan M. Wild,et al.  Nuclear energy density optimization: Large deformations , 2011, 1111.4344.

[32]  J. Piekarewicz,et al.  Accurate calibration of relativistic mean-field models: Correlating observables and providing meaningful theoretical uncertainties , 2011, 1109.1576.

[33]  Predictive power and theoretical uncertainties of mathematical modelling for nuclear physics , 2013 .

[34]  Erik Ostermann,et al.  Statistical And Computational Methods In Data Analysis , 2016 .

[35]  W. Nazarewicz,et al.  Information content of a new observable: The case of the nuclear neutron skin , 2010, 1002.4140.

[36]  J. E. Amaro,et al.  Partial Wave Analysis of Chiral NN Interactions , 2013, 1310.8167.

[37]  Albert Tarantola,et al.  Inverse problem theory - and methods for model parameter estimation , 2004 .

[38]  M. Kortelainen,et al.  Propagation of uncertainties in the Skyrme energy-density-functional model , 2013, 1301.6151.

[39]  R. Furnstahl,et al.  Neutron matter based on consistently evolved chiral three-nucleon interactions , 2013, 1301.7467.

[40]  W. Nazarewicz,et al.  Information content of the low-energy electric dipole strength: correlation analysis , 2012, 1211.1649.

[41]  J. E. Amaro,et al.  Statistical error analysis for phenomenological nucleon-nucleon potentials , 2014 .

[42]  Stefan M. Wild,et al.  Optimized chiral nucleon-nucleon interaction at next-to-next-to-leading order. , 2013, Physical review letters.

[43]  M. Kortelainen,et al.  The limits of the nuclear landscape , 2012, Nature.

[44]  J. Piekarewicz,et al.  Has a thick neutron skin in 208Pb been ruled out? , 2013, Physical review letters.

[45]  J. E. Amaro,et al.  Coarse grained NN potential with Chiral Two Pion Exchange , 2013, 1310.6972.

[46]  W. Nazarewicz,et al.  Electric dipole polarizability and the neutron skin , 2012, 1201.3807.

[47]  M. Bender,et al.  From finite nuclei to the nuclear liquid drop: Leptodermous expansion based on self-consistent mean-field theory , 2006 .