Journal
JOURNAL OF PHYSICS G-NUCLEAR AND PARTICLE PHYSICS
Volume 43, Issue 7, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0954-3899/43/7/074001
Keywords
Bayesian; effective field theory; uncertainty quantification
Categories
Funding
- National Science Foundation [PHY-1306250]
- US Department of Energy [DE-FG02-93ER40756]
- NUCLEI SciDAC Collaboration under DOE Grant [DE-SC0008533]
- Achievement Rewards for College Scientists Foundation
- Direct For Mathematical & Physical Scien
- Division Of Physics [1306250] Funding Source: National Science Foundation
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We present procedures based on Bayesian statistics for estimating, from data, the parameters of effective field theories (EFTs). The extraction of low-energy constants (LECs) is guided by theoretical expectations in a quantifiable way through the specification of Bayesian priors. A prior for natural-sized LECs reduces the possibility of overfitting, and leads to a consistent accounting of different sources of uncertainty. A set of diagnostic tools is developed that analyzes the fit and ensures that the priors do not bias the EFT parameter estimation. The procedures are illustrated using representative model problems, including the extraction of LECs for the nucleon-mass expansion in SU(2) chiral perturbation theory from synthetic lattice data.
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