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Title: 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:
 [1];  [2];  [1];  [1]
  1. Michigan State Univ., East Lansing, MI (United States)
  2. 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):
LA-UR-19-24496
Journal ID: ISSN 0031-9007; PRLTAO
Grant/Contract Number:  
FG52-08NA28552; 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 0031-9007
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 = {0031-9007},
number = 23,
volume = 122,
place = {United States},
year = {2019},
month = {6}
}

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Cited by: 3 works
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