Multivariate Fitting and the Error Matrix in Global Analysis of Data

Abstract

When a large body of data from diverse experiments is analyzed using a theoretical model with many parameters, the standard error matrix method and the general tools for evaluating errors may become inadequate. We present an iterative method that significantly improves the reliability of the error matrix calculation. To obtain even better estimates of the uncertainties on predictions of physical observables, we also present a Lagrange multiplier method that explores the entire parameter space and avoids the linear approximations assumed in conventional error propagation calculations. These methods are illustrated by an example from the global analysis of parton distribution functions.

13 pages, 5 figures, Latex; minor clarifications, fortran program made available; Normalization of Hessian matrix changed to HEP standard

References in corpus (4)

• Uncertainties of predictions from parton distribution functions II: the Hessian method
• Uncertainties of Predictions from Parton Distribution Functions I: the Lagrange Multiplier Method
• A new global analysis of deep inelastic scattering data
• A QCD analysis of HERA and fixed target structure function data

Cited by in corpus (98)

• Parton distributions for the LHC
• New Generation of Parton Distributions with Uncertainties from Global QCD Analysis
• EPS09 - a New Generation of NLO and LO Nuclear Parton Distribution Functions
• Measurement of the J/Psi Meson and b-Hadron Production Cross Sections in ppbar Collisions at sqrt s = 1960 GeV
• Inclusive Jet Production, Parton Distributions, and the Search for New Physics
• Global analysis of fragmentation functions for pions and kaons and their uncertainties
• EPPS16: Nuclear parton distributions with LHC data
• nCTEQ15 - Global analysis of nuclear parton distributions with uncertainties in the CTEQ framework
• The Physics of the B Factories
• Extraction of Spin-Dependent Parton Densities and Their Uncertainties
• Uncertainties of predictions from parton distribution functions II: the Hessian method
• Tevatron Run-1 Z Boson Data and Collins-Soper-Sterman Resummation Formalism
• Uncertainties of Predictions from Parton Distribution Functions I: the Lagrange Multiplier Method
• Global Analysis of Nuclear Parton Distributions
• Parton-to-Pion Fragmentation Reloaded
• The Structure of the Proton in the LHC Precision Era
• Precision measurement and interpretation of inclusive $W^{+}$, $W^{-}$ and $Z/{\gamma }^{\ast }$ production cross sections with the ATLAS detector
• Dynamical NNLO parton distributions
• Dynamical parton distributions of the nucleon and very small-x physics
• A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties
• Heavy Quark Mass Effects in Deep Inelastic Scattering and Global QCD Analysis
• Transverse momentum dependent gluon density from DIS precision data
• Parton-to-Kaon Fragmentation Revisited
• Sea quark and gluon polarization in the nucleon at NLO accuracy
• A Precision Measurement of the Inclusive ep Scattering Cross Section at HERA
• The Strange Parton Distribution of the Nucleon: Global Analysis and Applications
• Light-Cone Models for Intrinsic Charm and Bottom
• Neutrino Dimuon Production and the Strangeness Asymmetry of the Nucleon
• Open-source QCD analysis of nuclear parton distribution functions at NLO and NNLO
• Using hadron-in-jet data in a global analysis of $D^{\ast }$ fragmentation functions
• Neural network generated parametrizations of deeply virtual Compton form factors
• Structure Functions
• The hadronization of partons
• Nuclear PDFs After the First Decade of LHC Data
• Using world charged pion--nucleus scattering data to constrain an intranuclear cascade model
• Testing CCQE and 2p2h models in the NEUT neutrino interaction generator with published datasets from the MiniBooNE and MINERvA experiments
• NNLO nuclear parton distribution functions with electroweak-boson production data from the LHC
• $B$-hadron fragmentation functions at next-to-next-to-leading order from global analysis of $e^{+}{e}^{-}$ annihilation data
• Determination of pion and kaon fragmentation functions including spin asymmetries data in a global analysis
• The Quark and Gluon Structure of the Proton
• Nuclear parton distribution functions with uncertainties in a general mass variable flavor number scheme
• Inclusive Measurements of Inelastic Electron and Positron Scattering from Unpolarized Hydrogen and Deuterium Targets
• Data set diagonalization in a global fit
• Mapping the sensitivity of hadronic experiments to nucleon structure
• First determination of $D^{\ast +}$-meson fragmentation functions and their uncertainties at next-to-next-to-leading order
• Collider Inclusive Jet Data and the Gluon Distribution
• The Tensor Pomeron and Low-x Deep Inelastic Scattering
• Coherent photoproduction of $J/\psi$ in nucleus-nucleus collisions in the color dipole approach
• Constrained fit of the valence transversity distributions from dihadron production
• Nuclear parton density functions from jet production in DIS at the EIC
• Global analysis of fragmentation functions to charged hadrons with high-precision data from the LHC
• Uncertainties in pion and kaon fragmentation functions
• Higgs Boson Cross Section from CTEQ-TEA Global Analysis
• Parametrization dependence and Delta Chi-squared in parton distribution fitting
• A global extraction of the jet transport coefficient in cold nuclear matter
• Anatomy of a six-parameter fit to the $b\to s{\ell }^{+}{\ell }^{-}$ anomalies
• Investigation of Monte Carlo Uncertainties on Higgs Boson searches using Jet Substructure
• Exploring the Earth matter effect with atmospheric neutrinos in ice
• Simultaneous CTEQ-TEA extraction of PDFs and SMEFT parameters from jet and $t\bar{t}$ data
• ${\Lambda }_c^{+}$ fragmentation functions from pQCD approach and the Suzuki model
• Dipole model analysis of highest precision HERA data, including very low $Q^2$'s
• Differential Distributions for NLO Analyses of Charged Current Neutrino-Production of Charm
• New evaluation of axial nucleon form factor from electron- and neutrino-scattering data and impact on neutrino-nucleus cross-section
• Experimental consistency in parton distribution fitting
• Measurement of ${\sigma }_{\mathrm{ABS}}$ and ${\sigma }_{\mathrm{CX}}$ of ${\pi }^{+}$ on carbon by DUET
• Stability of NLO Global Analysis and Implications for Hadron Collider Physics
• Incoherent diffractive photoproduction of $J/\psi$ and ${\rm Y}$ on heavy nuclei in the color dipole approach
• Constraining Dark Matter Properties with Gamma-Rays from the Galactic Center with Fermi-LAT
• Charm Production and QCD Analysis at HERA and LHC
• Parton Distributions
• Automated calculation of Jet fragmentation at NLO in QCD
• Uncertainties of the Inclusive Higgs Production Cross Section at the Tevatron and the LHC
• Tests of goodness of fit to multiple data sets
• Simultaneous extraction of fragmentation functions of light charged hadrons with mass corrections
• Machine learning of log-likelihood functions in global analysis of parton distributions
• Polarized parton distributions from NLO QCD analysis of world DIS and SIDIS data
• Dynamical projections for the visualization of PDFSense data
• Light Gluino Constituents of Hadrons and a Global Analysis of Hadron Scattering Data
• QCD analysis of structure functions in deep inelastic neutrino-nucleon scattering without using the orthogonal polynomials approach
• Medium modified Fragmentation Functions with open source xFitter
• Quantifying statistical uncertainties in ab initio nuclear physics using Lagrange multipliers
• Markov Chain Monte Carlo technics applied to Parton Distribution Functions determination: proof of concept
• Uncertainties on Parton Related Quantities
• Parton distribution functions at LO, NLO and NNLO with correlated uncertainties between orders
• Fragmentation Functions for ${\Xi }^{-}/{\bar{\Xi }}^{+}$ Using Neural Networks
• Uncertainties of the CJK 5 Flavour LO Parton Distributions in the Real Photon
• Small-x behavior of non-singlet spin structure function and Bjorken sum rule with pQCD correction up to NNLO and Higher twist correction
• Global extraction of the parton-to-pion fragmentation functions at NLO accuracy in QCD
• Analysis of HERA data with a PDF parametrization inspired by quantum statistical mechanics
• LHC $Z^{‘}$ discovery potential for models with continuously distributed mass
• Determination of proton PDF uncertainties with Markov chain Monte Carlo
• Dynamical Parton Distributions of the Nucleon up to NNLO of QCD
• Proton structure at the LHC
• Determination of meson fragmentation functions in the Field-Feynman model
• QCD analysis of pion fragmentation functions in the xFitter framework
• Sea quark polarization and semi-inclusive DIS data
• An analysis of parton distributions in a pion with Bézier parametrizations
• Analyzing $t\bar{t}Z$-couplings at the future $e^{-}p$ collider