Direct Comparison between Bayesian and Frequentist Uncertainty Quantification for Nuclear Reactions
Abstract
Until recently, uncertainty quantification in low energy nuclear theory was typically performed using frequentist approaches. However in the last few years, the field has shifted toward Bayesian statistics for evaluating confidence intervals. Although there are statistical arguments to prefer the Bayesian approach, no direct comparison is available. In this work, we compare, directly and systematically, the frequentist and Bayesian approaches to quantifying uncertainties in direct nuclear reactions. Starting from identical initial assumptions, we determine confidence intervals associated with the elastic and the transfer process for both methods, which are evaluated against data via a comparison of the empirical coverage probabilities. Expectedly, the frequentist approach is not as flexible as the Bayesian approach in exploring parameter space and often ends up in a different minimum. We also show that the two methods produce significantly different correlations. In the end, the frequentist approach produces significantly narrower uncertainties on the considered observables than the Bayesian. Lastly, our study demonstrates that the uncertainties on the reaction observables considered here within the Bayesian approach represent reality more accurately than the much narrower uncertainties obtained using the standard frequentist approach.
 Authors:

 Michigan State Univ., East Lansing, MI (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Michigan State Univ., East Lansing, MI (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1526302
 Alternate Identifier(s):
 OSTI ID: 1542856; OSTI ID: 1546228
 Report Number(s):
 LAUR1924496
Journal ID: ISSN 00319007; PRLTAO
 Grant/Contract Number:
 FG5208NA28552; 89233218CNA000001; SC0018083; NA0002135
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review Letters
 Additional Journal Information:
 Journal Volume: 122; Journal Issue: 23; Journal ID: ISSN 00319007
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; uncertainty quantification; Bayesian
Citation Formats
King, G. B., Lovell, A. E., Neufcourt, L., and Nunes, F. M. Direct Comparison between Bayesian and Frequentist Uncertainty Quantification for Nuclear Reactions. United States: N. p., 2019.
Web. doi:10.1103/PhysRevLett.122.232502.
King, G. B., Lovell, A. E., Neufcourt, L., & Nunes, F. M. Direct Comparison between Bayesian and Frequentist Uncertainty Quantification for Nuclear Reactions. United States. doi:10.1103/PhysRevLett.122.232502.
King, G. B., Lovell, A. E., Neufcourt, L., and Nunes, F. M. Fri .
"Direct Comparison between Bayesian and Frequentist Uncertainty Quantification for Nuclear Reactions". United States. doi:10.1103/PhysRevLett.122.232502. https://www.osti.gov/servlets/purl/1526302.
@article{osti_1526302,
title = {Direct Comparison between Bayesian and Frequentist Uncertainty Quantification for Nuclear Reactions},
author = {King, G. B. and Lovell, A. E. and Neufcourt, L. and Nunes, F. M.},
abstractNote = {Until recently, uncertainty quantification in low energy nuclear theory was typically performed using frequentist approaches. However in the last few years, the field has shifted toward Bayesian statistics for evaluating confidence intervals. Although there are statistical arguments to prefer the Bayesian approach, no direct comparison is available. In this work, we compare, directly and systematically, the frequentist and Bayesian approaches to quantifying uncertainties in direct nuclear reactions. Starting from identical initial assumptions, we determine confidence intervals associated with the elastic and the transfer process for both methods, which are evaluated against data via a comparison of the empirical coverage probabilities. Expectedly, the frequentist approach is not as flexible as the Bayesian approach in exploring parameter space and often ends up in a different minimum. We also show that the two methods produce significantly different correlations. In the end, the frequentist approach produces significantly narrower uncertainties on the considered observables than the Bayesian. Lastly, our study demonstrates that the uncertainties on the reaction observables considered here within the Bayesian approach represent reality more accurately than the much narrower uncertainties obtained using the standard frequentist approach.},
doi = {10.1103/PhysRevLett.122.232502},
journal = {Physical Review Letters},
issn = {00319007},
number = 23,
volume = 122,
place = {United States},
year = {2019},
month = {6}
}
Web of Science
Works referenced in this record:
Quantifying truncation errors in effective field theory
journal, August 2015
 Furnstahl, R. J.; Klco, N.; Phillips, D. R.
 Physical Review C, Vol. 92, Issue 2
Bayesian truncation errors in chiral effective field theory: Nucleonnucleon observables
journal, August 2017
 Melendez, J. A.; Wesolowski, S.; Furnstahl, R. J.
 Physical Review C, Vol. 96, Issue 2
Bayesian approach to modelbased extrapolation of nuclear observables
journal, September 2018
 Neufcourt, Léo; Cao, Yuchen; Nazarewicz, Witold
 Physical Review C, Vol. 98, Issue 3
Precision Mass Measurements of NeutronRich Neodymium and Samarium Isotopes and Their Role in Understanding RareEarth Peak Formation
journal, June 2018
 Orford, R.; Vassh, N.; Clark, J. A.
 Physical Review Letters, Vol. 120, Issue 26
Neutron Star Tidal Deformabilities Constrained by Nuclear Theory and Experiment
journal, August 2018
 Lim, Yeunhwan; Holt, Jeremy W.
 Physical Review Letters, Vol. 121, Issue 6
Constraining transfer cross sections using Bayes' theorem
journal, June 2018
 Lovell, A. E.; Nunes, F. M.
 Physical Review C, Vol. 97, Issue 6
NucleonNucleus OpticalModel Parameters, $A>\mathrm{}40\mathrm{}$ , $E<\mathrm{}50\mathrm{}$ MeV
journal, June 1969
 Becchetti, F. D.; Greenlees, G. W.
 Physical Review, Vol. 182, Issue 4
A global nucleon optical model potential
journal, March 1991
 Varner, R. L.; Thompson, W. J.; McAbee, T. L.
 Physics Reports, Vol. 201, Issue 2
Local and global nucleon optical models from 1 keV to 200 MeV
journal, January 2003
 Koning, A. J.; Delaroche, J. P.
 Nuclear Physics A, Vol. 713, Issue 34
Uncertainty quantification for optical model parameters
journal, February 2017
 Lovell, A. E.; Nunes, F. M.; Sarich, J.
 Physical Review C, Vol. 95, Issue 2
Uncertainty quantification due to optical potentials in models for ( $d,p$ ) reactions
journal, October 2018
 King, G. B.; Lovell, A. E.; Nunes, F. M.
 Physical Review C, Vol. 98, Issue 4
Nuclear sizes in 40, 44, 48Ca
journal, June 1972
 Lombardi, J. C.; Boyd, R. N.; Arking, R.
 Nuclear Physics A, Vol. 188, Issue 1
Asymmetry dependence of nucleon correlations in spherical nuclei extracted from a dispersiveopticalmodel analysis
journal, June 2011
 Mueller, J. M.; Charity, R. J.; Shane, R.
 Physical Review C, Vol. 83, Issue 6
Elastic scattering of protons from ${}_{}{}^{40}{}_{}{}^{}$ , 42 , 44 , 48 Ca from 20 to 50 MeV and nuclear matter radii
journal, May 1986
 McCamis, R. H.; Nasr, T. N.; Birchall, J.
 Physical Review C, Vol. 33, Issue 5
${}_{}{}^{90,92,94}{}_{}{}^{}\mathrm{Zr}(p,{p}^{\prime})$ Reactions at 12.7 MeV
journal, April 1968
 Dickens, J. K.; Eichler, E.; Satchler, G. R.
 Physical Review, Vol. 168, Issue 4
Neutron scattering from 90,91,92,94Zr
journal, October 1990
 Wang, Y.; Rapaport, J.
 Nuclear Physics A, Vol. 517, Issue 2
Scattering of 22.5MeV Protons from Zirconium and the Symmetry Term in the Nuclear Optical Potential
journal, August 1964
 Ball, J. B.; Fulmer, C. B.; Bassel, R. H.
 Physical Review, Vol. 135, Issue 3B
Proton Elastic Scattering Measurements at 16 MeV with OpticalModel Analysis
journal, March 1972
 Makofske, W.; Greenlees, G. W.; Liers, H. S.
 Physical Review C, Vol. 5, Issue 3
Opticalmodel analysis of $p+{}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ elastic scattering from 15  1000 MeV
journal, July 1974
 van Oers, W. T. H.; Haw, Huang; Davison, N. E.
 Physical Review C, Vol. 10, Issue 1
Coupled reaction channels calculations in nuclear physics
journal, April 1988
 Thompson, Ian J.
 Computer Physics Reports, Vol. 7, Issue 4
An approximate threebody theory of deuteron stripping
journal, December 1974
 Johnson, R. C.; Tandy, P. C.
 Nuclear Physics A, Vol. 235, Issue 1
Transfer reaction code with nonlocal interactions
journal, October 2016
 Titus, L. J.; Ross, A.; Nunes, F. M.
 Computer Physics Communications, Vol. 207
Forbidden transitions in the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(d,p){}_{}{}^{49}{}_{}{}^{}\mathrm{Ca}$ reaction
journal, September 1975
 Metz, W. D.; Callender, W. D.; Bockelman, C. K.
 Physical Review C, Vol. 12, Issue 3