Quantifying correlated truncation errors in effective field theory
Abstract
Effective field theories (EFTs) organize the description of complex systems into an infinite sequence of decreasing importance. Predictions are made with a finite number of terms, which induces a truncation error that is often left unquantified. Here, we formalize the notion of EFT convergence and propose a Bayesian truncation error model for predictions that are correlated across the independent variables, e.g., energy or scattering angle. Central to our approach are Gaussian processes that encode both the naturalness and correlation structure of EFT coefficients. Our use of Gaussian processes permits efficient and accurate assessment of credible intervals, allows EFT fits to easily include correlated theory errors, and provides analytic posteriors for physical EFT-related quantities such as the expansion parameter. Furthermore, we demonstrate that model-checking diagnostics—applied to the case of multiple curves—are powerful tools for EFT validation. As an example, we assess a set of nucleon-nucleon scattering observables in chiral EFT. In an effort to be self-contained, appendices include thorough derivations of our statistical results. Our methods are packaged in Python code, called gsum, that is available for download on GitHub.
- Authors:
-
- The Ohio State Univ., Columbus, OH (United States)
- Ohio Univ., Athens, OH (United States); Technical Univ. of Darmstadt (Germany); GSI-Darmstadt (Germany)
- Salisbury Univ., MD (United States)
- Publication Date:
- Research Org.:
- The Ohio State Univ., Columbus, OH (United States); Michigan State Univ., East Lansing, MI; Oak Ridge Associated Univ., Oak Ridge, TN (United States) (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Workforce Development for Teachers and Scientists (WDTS); USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)
- OSTI Identifier:
- 1630533
- Grant/Contract Number:
- SC0018083; PHY-1614460; RC107839-OSU; SC0014664; FG02-93ER-40756
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review C
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 4; Journal ID: ISSN 2469-9985
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Melendez, J. A., Furnstahl, R. J., Phillips, D. R., Pratola, M. T., and Wesolowski, S. Quantifying correlated truncation errors in effective field theory. United States: N. p., 2019.
Web. doi:10.1103/PhysRevC.100.044001.
Melendez, J. A., Furnstahl, R. J., Phillips, D. R., Pratola, M. T., & Wesolowski, S. Quantifying correlated truncation errors in effective field theory. United States. https://doi.org/10.1103/PhysRevC.100.044001
Melendez, J. A., Furnstahl, R. J., Phillips, D. R., Pratola, M. T., and Wesolowski, S. Thu .
"Quantifying correlated truncation errors in effective field theory". United States. https://doi.org/10.1103/PhysRevC.100.044001. https://www.osti.gov/servlets/purl/1630533.
@article{osti_1630533,
title = {Quantifying correlated truncation errors in effective field theory},
author = {Melendez, J. A. and Furnstahl, R. J. and Phillips, D. R. and Pratola, M. T. and Wesolowski, S.},
abstractNote = {Effective field theories (EFTs) organize the description of complex systems into an infinite sequence of decreasing importance. Predictions are made with a finite number of terms, which induces a truncation error that is often left unquantified. Here, we formalize the notion of EFT convergence and propose a Bayesian truncation error model for predictions that are correlated across the independent variables, e.g., energy or scattering angle. Central to our approach are Gaussian processes that encode both the naturalness and correlation structure of EFT coefficients. Our use of Gaussian processes permits efficient and accurate assessment of credible intervals, allows EFT fits to easily include correlated theory errors, and provides analytic posteriors for physical EFT-related quantities such as the expansion parameter. Furthermore, we demonstrate that model-checking diagnostics—applied to the case of multiple curves—are powerful tools for EFT validation. As an example, we assess a set of nucleon-nucleon scattering observables in chiral EFT. In an effort to be self-contained, appendices include thorough derivations of our statistical results. Our methods are packaged in Python code, called gsum, that is available for download on GitHub.},
doi = {10.1103/PhysRevC.100.044001},
journal = {Physical Review C},
number = 4,
volume = 100,
place = {United States},
year = {2019},
month = {10}
}
Web of Science
Figures / Tables:

Works referenced in this record:
Diagnostics for Gaussian Process Emulators
journal, November 2009
- Bastos, Leonardo S.; O’Hagan, Anthony
- Technometrics, Vol. 51, Issue 4
Nuclear forces from chiral lagrangians
journal, November 1990
- Weinberg, Steven
- Physics Letters B, Vol. 251, Issue 2
Design and analysis of computer experiments
conference, September 1998
- Booker, Andrew
- 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
The effect of the nugget on Gaussian process emulators of computer models
journal, December 2012
- Andrianakis, Ioannis; Challenor, Peter G.
- Computational Statistics & Data Analysis, Vol. 56, Issue 12
Bayes in the sky: Bayesian inference and model selection in cosmology
journal, March 2008
- Trotta, Roberto
- Contemporary Physics, Vol. 49, Issue 2
Design and analysis of computer experiments
journal, December 2010
- Kuhnt, Sonja; Steinberg, David M.
- AStA Advances in Statistical Analysis, Vol. 94, Issue 4
A Computationally Stable Approach to Gaussian Process Interpolation of Deterministic Computer Simulation Data
journal, November 2011
- Ranjan, Pritam; Haynes, Ronald; Karsten, Richard
- Technometrics, Vol. 53, Issue 4
Bayesian parameter estimation for effective field theories
journal, May 2016
- Wesolowski, S.; Klco, N.; Furnstahl, R. J.
- Journal of Physics G: Nuclear and Particle Physics, Vol. 43, Issue 7
Precision Nucleon-Nucleon Potential at Fifth Order in the Chiral Expansion
journal, September 2015
- Epelbaum, E.; Krebs, H.; Meißner, U. -G.
- Physical Review Letters, Vol. 115, Issue 12
Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order
journal, May 2018
- Reinert, P.; Krebs, H.; Epelbaum, E.
- The European Physical Journal A, Vol. 54, Issue 5
Inference for variograms
journal, October 2013
- Bowman, Adrian W.; Crujeiras, Rosa M.
- Computational Statistics & Data Analysis, Vol. 66
Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
journal, May 2015
- Epelbaum, E.; Krebs, H.; Meißner, U. -G.
- The European Physical Journal A, Vol. 51, Issue 5
Meaningful characterisation of perturbative theoretical uncertainties
journal, September 2011
- Cacciari, Matteo; Houdeau, Nicolas
- Journal of High Energy Physics, Vol. 2011, Issue 9
Design and Analysis of Computer Experiments
journal, November 1989
- Sacks, Jerome; Welch, William J.; Mitchell, Toby J.
- Statistical Science, Vol. 4, Issue 4
On the condition number of covariance matrices in kriging, estimation, and simulation of random fields
journal, January 1994
- Ababou, Rachid; Bagtzoglou, Amvrossios C.; Wood, Eric F.
- Mathematical Geology, Vol. 26, Issue 1
Interpolation of Spatial Data
journal, September 2018
- Aliyev, Rae Zh
- Biomedical Journal of Scientific & Technical Research, Vol. 9, Issue 1
Probabilistic programming in Python using PyMC3
journal, January 2016
- Salvatier, John; Wiecki, Thomas V.; Fonnesbeck, Christopher
- PeerJ Computer Science, Vol. 2
Effective chiral lagrangians for nucleon-pion interactions and nuclear forces
journal, September 1991
- Weinberg, Steven
- Nuclear Physics B, Vol. 363, Issue 1
Fitting variogram models by weighted least squares
journal, July 1985
- Cressie, Noel
- Journal of the International Association for Mathematical Geology, Vol. 17, Issue 5
Statistics for spatial data
journal, April 1993
- Haining, Robert
- Computers & Geosciences, Vol. 19, Issue 4
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
Exploring Bayesian parameter estimation for chiral effective field theory using nucleon–nucleon phase shifts
journal, February 2019
- Wesolowski, S.; Furnstahl, R. J.; Melendez, J. A.
- Journal of Physics G: Nuclear and Particle Physics, Vol. 46, Issue 4
Bayesian truncation errors in chiral effective field theory: Nucleon-nucleon observables
journal, August 2017
- Melendez, J. A.; Wesolowski, S.; Furnstahl, R. J.
- Physical Review C, Vol. 96, Issue 2
High-quality two-nucleon potentials up to fifth order of the chiral expansion
journal, August 2017
- Entem, D. R.; Machleidt, R.; Nosyk, Y.
- Physical Review C, Vol. 96, Issue 2
Bayes in the sky: Bayesian inference and model selection in cosmology
text, January 2008
- Trotta, Roberto
- arXiv
A Computationally Stable Approach to Gaussian Process Interpolation of Deterministic Computer Simulation Data
text, January 2010
- Ranjan, Pritam; Haynes, Ronald; Karsten, Richard
- arXiv
Meaningful characterisation of perturbative theoretical uncertainties
text, January 2011
- Cacciari, Matteo; Houdeau, Nicolas
- arXiv
Precision nucleon-nucleon potential at fifth order in the chiral expansion
text, January 2014
- Epelbaum, E.; Krebs, H.; Meißner, U. -G.
- arXiv
Figures / Tables found in this record: