Reconstruction of Monte Carlo replicas from Hessian parton distributions
Abstract
We explore connections between two common methods for quantifying the uncertainty in parton distribution functions (PDFs), based on the Hessian error matrix and Monte-Carlo sampling. CT14 parton distributions in the Hessian representation are converted into Monte-Carlo replicas by a numerical method that reproduces important properties of CT14 Hessian PDFs: the asymmetry of CT14 uncertainties and positivity of individual parton distributions. The ensembles of CT14 Monte-Carlo replicas constructed this way at NNLO and NLO are suitable for various collider applications, such as cross section reweighting. Master formulas for computation of asymmetric standard deviations in the Monte-Carlo representation are derived. A correction is proposed to address a bias in asymmetric uncertainties introduced by the Taylor series approximation. A numerical program is made available for conversion of Hessian PDFs into Monte-Carlo replicas according to normal, log-normal, and Watt-Thorne sampling procedures.
Keywords
Cite
@article{arxiv.1607.06066,
title = {Reconstruction of Monte Carlo replicas from Hessian parton distributions},
author = {Tie-Jiun Hou and Jun Gao and Joey Huston and Pavel Nadolsky and Carl Schmidt and Daniel Stump and Bo-Ting Wang and Ke-Ping Xie and Sayipjamal Dulat and Jon Pumplin and C. -P. Yuan},
journal= {arXiv preprint arXiv:1607.06066},
year = {2017}
}
Comments
21 pages, 10 figures; final JHEP version, extended Sec. 2 to discuss sampling of asymmetric PDF replica distributions with imposed positivity constraints