Markov Chain Monte Carlo technics applied to Parton Distribution Functions determination: proof of concept
arXiv:1701.07678 · doi:10.1103/PhysRevD.96.014015
Abstract
We present a new procedure to determine Parton Distribution Functions (PDFs), based on Markov Chain Monte Carlo (MCMC) methods. The aim of this paper is to show that we can replace the standard minimization by procedures grounded on Statistical Methods, and on Bayesian inference in particular, thus offering additional insight into the rich field of PDFs determination. After a basic introduction to these technics, we introduce the algorithm we have chosen to implement -- namely Hybrid (or Hamiltonian) Monte Carlo. This algorithm, initially developed for Lattice QCD, turns out to be very interesting when applied to PDFs determination by global analyses; we show that it allows to circumvent the difficulties due to the high dimensionality of the problem, in particular concerning the acceptance. A first feasibility study is performed and presented, which indicates that Markov Chain Monte Carlo can successfully be applied to the extraction of PDFs and of their uncertainties.
arXiv comment17 pages, 9 figures. Published in Phys. Rev. D
References in corpus (25)
- New Generation of Parton Distributions with Uncertainties from Global QCD Analysis
- MCMC using Hamiltonian dynamics
- Improved Parton Distributions from Global Analysis of Recent Deep Inelastic Scattering and Inclusive Jet Data
- Parton Physics on Euclidean Lattice
- Combined Measurement and QCD Analysis of the Inclusive ep Scattering Cross Sections at HERA
- Uncertainties of predictions from parton distribution functions II: the Hessian method
- Uncertainties of predictions from parton distributions. I: experimental errors
- TMD Parton Distribution and Fragmentation Functions with QCD Evolution
- Monte Carlo errors with less errors
- QCDNUM: Fast QCD Evolution and Convolution
- Uncertainties of Predictions from Parton Distribution Functions I: the Lagrange Multiplier Method
- Measurement and QCD Analysis of Neutral and Charged Current Cross Sections at HERA
- Uncertainties of predictions from parton distributions. I: Theoretical errors
- A ZEUS next-to-leading-order QCD analysis of data on deep inelastic scattering
- Implications of Hadron Collider Observables on Parton Distribution Function Uncertainties
- Multivariate Fitting and the Error Matrix in Global Analysis of Data
- Measurement of the Inclusive ep Scattering Cross Section at Low Q^2 and x at HERA
- An NLO QCD analysis of inclusive cross-section and jet-production data from the ZEUS experiment
- Neural network determination of parton distributions: the nonsinglet case
- A Precision Measurement of the Inclusive ep Scattering Cross Section at HERA
- A Markov Chain Monte Carlo for Galactic Cosmic Ray physics: I. Method and results for the Leaky Box Model
- Large Transverse Momentum Jet Production and the Gluon Distribution Inside the Proton
- Consistent Treatment of Charm Evolution in Deep Inelastic Scattering
- Generalized universality of higher transverse moments of quark transverse momentum dependent correlators
- Non-collinearity in high energy processes