Determination of proton PDF uncertainties with Markov chain Monte Carlo

Abstract

We present an analysis of parton distribution functions (PDFs) of the proton using Markov Chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes' theorem and thus provides a means to directly sample the underlying probability distribution - in this case the probability distribution of the PDF parameters. This allows for a straightforward propagation of the resulting uncertainties into any PDF-dependent observable, preserving their simple probabilistic interpretation. In our analysis we include a broad set of deep inelastic scattering data from HERA, BCDMS and NMC experiments along with the Drell-Yan, $W$ and $Z$ boson data from LHC and Tevatron experiments, which combined with theoretical calculations at next-to-next-to-leading order in QCD allow for realistic determination of PDFs. The main focus of this analysis is to explore alternative methods for PDF uncertainty estimation that are more firmly grounded in statistical principles. We show that the flexibility of the Bayes framework, allowing e.g. to account for non-Gaussianity or inconsistencies of data sets, is crucial to extract realistic uncertainties when such assumptions are not fulfilled. We also demonstrate that MCMC allows one to determine the $\Delta {\chi }^2$ value corresponding to a given confidence level in the sample, which can in turn be used as a statistically well-founded tolerance criterion used in the Hessian method, thus addressing one of its main long-standing drawbacks.

20 pages, 9 figures, matches published version: Phys. Rev. D 113, 054049

References in corpus (21)

• Parton distributions for the LHC
• Vector boson pair production at the LHC
• Parton distributions from LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs
• The Path to Proton Structure at One-Percent Accuracy
• Dynamical parton distributions of the nucleon and very small-x physics
• Measurement of the shape of the boson rapidity distribution for p\bar{p}-> Z/gamma*-> e+e- +X events produced at sqrt(s) of 1.96 TeV
• Parton Distributions in Nucleons and Nuclei
• Approximate N${}^3$LO Parton Distribution Functions with Theoretical Uncertainties: MSHT20aN${}^3$LO PDFs
• APFEL Web: a web-based application for the graphical visualization of parton distribution functions
• A Markov Chain Monte Carlo for Galactic Cosmic Ray physics: I. Method and results for the Leaky Box Model
• An extensive survey of the estimation of uncertainties from missing higher orders in perturbative calculations
• Impact of heavy quark and quarkonium data on nuclear gluon PDFs
• Probabilistic definition of the perturbative theoretical uncertainty from missing higher orders
• Parton distributions with scale uncertainties: a MonteCarlo sampling approach
• Compatibility of Neutrino DIS Data and Its Impact on Nuclear Parton Distribution Functions
• Heavy Quark Production in the ACOT Scheme at NNLO and N3LO
• On the determination of uncertainties in parton densities
• Machine learning of log-likelihood functions in global analysis of parton distributions
• Systematic uncertainties from higher-twist corrections in DIS at large x
• Robust estimates of theoretical uncertainties at fixed-order in perturbation theory
• PartonDensity.jl: a novel parton density determination code