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Bayesian Inference with Gaussian Processes for the Determination of Parton Distribution Functions

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arxiv 2404.07573 v2 pith:S6DUFB2J submitted 2024-04-11 hep-ph hep-lat

Alessandro Candido , Luigi Del Debbio , Tommaso Giani , Giacomo Petrillo This is my paper · ORCID
classification hep-phhep-lat
keywords bayesiandeterminationdiscussdistributionmethodologydataenteringfunctions
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We discuss a Bayesian methodology for the solution of the inverse problem underlying the determination of parton distribution functions (PDFs). In our approach, Gaussian Processes (GPs) are used to model the PDF prior, while Bayes theorem is used in order to determine the posterior distribution of the PDFs given a set of data. We discuss the general formalism, the Bayesian inference at the level of both parameters and hyperparameters, and the simplifications which occur when the observable entering the analysis is linear in the PDF. We benchmark the new methodology in two simple examples for the determination of a single PDF flavor from a set of Deep Inelastic Scattering (DIS) data and from a set of equal-time correlators computed using lattice QCD. We discuss our results, showing how the proposed methodology allows for a well-defined statistical interpretation of the different sources of errors entering the PDF uncertainty, and how results can be validated a posteriori.

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Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Normalizing Flows to Reconstruct Pseudo-PDFs

    hep-lat 2026-07 conditional novelty 6.0 of 10

    An invertible neural network trained on Gaussian-process-prior samples reconstructs pseudo-PDFs from limited Ioffe-time data in closure tests, with constraints preserved but latent-dimension-dependent extrapolation.

  2. Quantitative Understanding of PDF Fits and their Uncertainties

    hep-ph 2025-12 conditional novelty 6.0 of 10

    After an initial transient, a PDF-fitting neural network's output obeys f_t = U(t) f_0 + V(t) Y, a linear blend of the initial network and the data with explicit time-dependent operators.

  3. Gradient flow for parton distribution functions: first application to the pion

    hep-lat 2025-09 conditional novelty 6.0 of 10

    Pion PDF moment ratios up to <x^5> were extracted from lattice QCD with gradient flow and agree with phenomenological fits.

  4. A simple non-parametric reconstruction of parton distributions from limited Fourier information

    hep-lat 2024-12 conditional novelty 5.0 of 10

    A fixed-hyperparameter Gaussian-process prior recovers parton distributions from limited Ioffe-time data and yields more realistic small-x uncertainties than simple parametric fits.

  5. Comment on "LaMET's Asymptotic Extrapolation vs. Inverse Problem"

    hep-lat 2025-06 conditional novelty 4.0 of 10

    The paper defends the inverse-problem view of LaMET reconstructions and argues that rigid parametric extrapolations underestimate PDF uncertainties when lattice data are noisy.

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